diff --git a/.circleci/config.yml b/.circleci/config.yml
index 3b626d79b..d9807a81d 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -1,6 +1,7 @@
 # Circle CI configuration file
 # https://circleci.com/docs/
 
+---
 version: 2.1
 
 
@@ -8,7 +9,7 @@ version: 2.1
 # Define some common steps as YAML anchors.
 #
 
-apt-run:  &apt-install
+apt-run: &apt-install
   name: Install apt packages
   command: |
     apt-get -qq update
@@ -17,15 +18,18 @@ apt-run:  &apt-install
       g++ \
       make
 
-env-run:  &env-setup
+env-run: &env-setup
   # Create the basic testing environment
   # Mixing conda-forge and defaults in root is a recipe for trouble, so create
   # a separate environment.
   name: Setup conda environment
   command: |
-    conda config --set always_yes yes --set changeps1 no --set show_channel_urls yes
-    conda create -n test-environment python=$PYTHON_VERSION
+    conda config \
+        --set always_yes yes \
+        --set changeps1 no \
+        --set show_channel_urls yes
     conda config --add channels conda-forge
+    conda create -n test-environment python=$PYTHON_VERSION
 
 deps-run: &deps-install
   name: Install Python dependencies
diff --git a/lib/cartopy/crs.py b/lib/cartopy/crs.py
index 1505819e2..3c26b7243 100644
--- a/lib/cartopy/crs.py
+++ b/lib/cartopy/crs.py
@@ -39,42 +39,7 @@
 WGS84_SEMIMINOR_AXIS = 6356752.3142
 
 
-def _safe_pj_transform_611(src_crs, tgt_crs, x, y, z=None, trap=True):
-    """
-    Workaround bug in Proj 6.1.1+ with +to_meter on +proj=ob_tran.
-
-    See https://github.com/OSGeo/proj#1782.
-    """
-    lonlat = ('latlon', 'latlong', 'lonlat', 'longlat')
-
-    if (
-        src_crs.proj4_params.get('proj', '') == 'ob_tran' and
-        src_crs.proj4_params.get('o_proj', '') in lonlat and
-        'to_meter' in src_crs.proj4_params
-    ):
-        x *= src_crs.proj4_params['to_meter']
-        y *= src_crs.proj4_params['to_meter']
-
-    transformer = Transformer.from_crs(src_crs, tgt_crs, always_xy=True)
-    transformed_coords = transformer.transform(x, y, z, errcheck=trap)
-    if z is None:
-        xx, yy = transformed_coords
-        zz = 0
-    else:
-        xx, yy, zz = transformed_coords
-
-    if (
-        tgt_crs.proj4_params.get('proj', '') == 'ob_tran' and
-        tgt_crs.proj4_params.get('o_proj', '') in lonlat and
-        'to_meter' in tgt_crs.proj4_params
-    ):
-        xx /= tgt_crs.proj4_params['to_meter']
-        yy /= tgt_crs.proj4_params['to_meter']
-
-    return xx, yy, zz
-
-
-def _safe_pj_transform_pre_611(src_crs, tgt_crs, x, y, z=None, trap=True):
+def _safe_pj_transform(src_crs, tgt_crs, x, y, z=None, trap=True):
     transformer = Transformer.from_crs(src_crs, tgt_crs, always_xy=True)
     transformed_coords = transformer.transform(x, y, z, errcheck=trap)
     if z is None:
@@ -85,12 +50,6 @@ def _safe_pj_transform_pre_611(src_crs, tgt_crs, x, y, z=None, trap=True):
     return xx, yy, zz
 
 
-if (6, 1, 1) <= PROJ_VERSION < (6, 3, 0):
-    _safe_pj_transform = _safe_pj_transform_611
-else:
-    _safe_pj_transform = _safe_pj_transform_pre_611
-
-
 class Globe(object):
     """
     Define an ellipsoid and, optionally, how to relate it to the real world.
@@ -1465,12 +1424,8 @@ def __init__(self, central_longitude=0.0, central_latitude=0.0,
                         ('lat_0', central_latitude), ('k', scale_factor),
                         ('x_0', false_easting), ('y_0', false_northing),
                         ('units', 'm')]
-        if PROJ_VERSION < (6, 0, 0):
-            if not approx:
-                proj4_params[0] = ('proj', 'etmerc')
-        else:
-            if approx:
-                proj4_params += [('approx', None)]
+        if approx:
+            proj4_params += [('approx', None)]
         super().__init__(proj4_params, globe=globe)
 
         self.threshold = 1e4
@@ -2018,25 +1973,6 @@ def __init__(self, central_latitude=0.0, central_longitude=0.0,
                  false_easting=0.0, false_northing=0.0,
                  true_scale_latitude=None,
                  scale_factor=None, globe=None):
-        # Warn when using Stereographic with proj < 5.0.0 due to
-        # incorrect transformation with lon_0=0 (see
-        # https://github.com/OSGeo/proj.4/issues/194).
-        if central_latitude == 0:
-            if PROJ_VERSION != ():
-                if PROJ_VERSION < (5, 0, 0):
-                    warnings.warn(
-                        'The Stereographic projection in Proj older than '
-                        '5.0.0 incorrectly transforms points when '
-                        'central_latitude=0. Use this projection with '
-                        'caution.',
-                        stacklevel=2)
-            else:
-                warnings.warn(
-                    'Cannot determine Proj version. The Stereographic '
-                    'projection may be unreliable and should be used with '
-                    'caution.',
-                    stacklevel=2)
-
         proj4_params = [('proj', 'stere'), ('lat_0', central_latitude),
                         ('lon_0', central_longitude),
                         ('x_0', false_easting), ('y_0', false_northing)]
@@ -2115,19 +2051,6 @@ class Orthographic(Projection):
 
     def __init__(self, central_longitude=0.0, central_latitude=0.0,
                  globe=None):
-        if PROJ_VERSION != ():
-            if (5, 0, 0) <= PROJ_VERSION < (5, 1, 0):
-                warnings.warn(
-                    'The Orthographic projection in the v5.0.x series of Proj '
-                    'incorrectly transforms points. Use this projection with '
-                    'caution.',
-                    stacklevel=2)
-        else:
-            warnings.warn(
-                'Cannot determine Proj version. The Orthographic projection '
-                'may be unreliable and should be used with caution.',
-                stacklevel=2)
-
         proj4_params = [('proj', 'ortho'), ('lon_0', central_longitude),
                         ('lat_0', central_latitude)]
         super().__init__(proj4_params, globe=globe)
@@ -2350,11 +2273,6 @@ def __init__(self, central_longitude=0, false_easting=None,
             If omitted, a default globe is created.
 
         """
-        if PROJ_VERSION < (5, 2, 0):
-            _proj_ver = '.'.join(str(v) for v in PROJ_VERSION)
-            raise ValueError('The EqualEarth projection requires Proj version '
-                             f'5.2.0, but you are using {_proj_ver}.')
-
         proj_params = [('proj', 'eqearth'), ('lon_0', central_longitude)]
         super().__init__(proj_params, central_longitude,
                          false_easting=false_easting,
@@ -2436,22 +2354,6 @@ def __init__(self, central_longitude=0, globe=None,
                 This projection does not handle elliptical globes.
 
         """
-        # Warn when using Robinson with proj 4.8 due to discontinuity at
-        # 40 deg N introduced by incomplete fix to issue #113 (see
-        # https://github.com/OSGeo/proj.4/issues/113).
-        if PROJ_VERSION != ():
-            if (4, 8) <= PROJ_VERSION < (4, 9):
-                warnings.warn('The Robinson projection in the v4.8.x series '
-                              'of Proj contains a discontinuity at '
-                              '40 deg latitude. Use this projection with '
-                              'caution.',
-                              stacklevel=2)
-        else:
-            warnings.warn('Cannot determine Proj version. The Robinson '
-                          'projection may be unreliable and should be used '
-                          'with caution.',
-                          stacklevel=2)
-
         proj4_params = [('proj', 'robin'), ('lon_0', central_longitude)]
         super().__init__(proj4_params, central_longitude,
                          false_easting=false_easting,
@@ -2543,11 +2445,6 @@ def __init__(self, central_longitude=0, globe=None, emphasis='land'):
             super().__init__(proj4_params, globe=globe)
 
         elif emphasis == 'ocean':
-            if PROJ_VERSION < (7, 1, 0):
-                _proj_ver = '.'.join(str(v) for v in PROJ_VERSION)
-                raise ValueError('The Interrupted Goode Homolosine ocean '
-                                 'projection requires Proj version 7.1.0, '
-                                 f'but you are using {_proj_ver}')
             proj4_params = [('proj', 'igh_o'), ('lon_0', central_longitude)]
             super().__init__(proj4_params, globe=globe)
 
@@ -2929,22 +2826,6 @@ def __init__(self, central_longitude=0.0, central_latitude=0.0,
             globe is created.
 
         """
-        # Warn when using Azimuthal Equidistant with proj < 4.9.2 due to
-        # incorrect transformation past 90 deg distance (see
-        # https://github.com/OSGeo/proj.4/issues/246).
-        if PROJ_VERSION != ():
-            if PROJ_VERSION < (4, 9, 2):
-                warnings.warn('The Azimuthal Equidistant projection in Proj '
-                              'older than 4.9.2 incorrectly transforms points '
-                              'farther than 90 deg from the origin. Use this '
-                              'projection with caution.',
-                              stacklevel=2)
-        else:
-            warnings.warn('Cannot determine Proj version. The Azimuthal '
-                          'Equidistant projection may be unreliable and '
-                          'should be used with caution.',
-                          stacklevel=2)
-
         proj4_params = [('proj', 'aeqd'), ('lon_0', central_longitude),
                         ('lat_0', central_latitude),
                         ('x_0', false_easting), ('y_0', false_northing)]
diff --git a/lib/cartopy/tests/crs/test_equal_earth.py b/lib/cartopy/tests/crs/test_equal_earth.py
index f2d4ac983..4ab904d90 100644
--- a/lib/cartopy/tests/crs/test_equal_earth.py
+++ b/lib/cartopy/tests/crs/test_equal_earth.py
@@ -16,10 +16,6 @@
 from .helpers import check_proj_params
 
 
-pytestmark = pytest.mark.skipif(ccrs.PROJ_VERSION < (5, 2, 0),
-                                reason='Proj is too old.')
-
-
 def test_default():
     eqearth = ccrs.EqualEarth()
     other_args = {'ellps=WGS84', 'lon_0=0'}
diff --git a/lib/cartopy/tests/crs/test_interrupted_goode_homolosine.py b/lib/cartopy/tests/crs/test_interrupted_goode_homolosine.py
index c36c24963..4b51492f0 100644
--- a/lib/cartopy/tests/crs/test_interrupted_goode_homolosine.py
+++ b/lib/cartopy/tests/crs/test_interrupted_goode_homolosine.py
@@ -18,8 +18,6 @@
 
 @pytest.mark.parametrize("emphasis", ["land", "ocean"])
 def test_default(emphasis):
-    if emphasis == "ocean" and ccrs.PROJ_VERSION < (7, 1, 0):
-        pytest.skip()
     igh = ccrs.InterruptedGoodeHomolosine(emphasis=emphasis)
     other_args = {"ellps=WGS84", "lon_0=0"}
     if emphasis == "land":
@@ -36,8 +34,6 @@ def test_default(emphasis):
 
 @pytest.mark.parametrize("emphasis", ["land", "ocean"])
 def test_eccentric_globe(emphasis):
-    if emphasis == "ocean" and ccrs.PROJ_VERSION < (7, 1, 0):
-        pytest.skip()
     globe = ccrs.Globe(semimajor_axis=1000, semiminor_axis=500, ellipse=None)
     igh = ccrs.InterruptedGoodeHomolosine(globe=globe, emphasis=emphasis)
     other_args = {"a=1000", "b=500", "lon_0=0"}
@@ -55,8 +51,6 @@ def test_eccentric_globe(emphasis):
     [("land", -10.0), ("land", 10.0), ("ocean", -10.0), ("ocean", 10.0)],
 )
 def test_central_longitude(emphasis, lon):
-    if emphasis == "ocean" and ccrs.PROJ_VERSION < (7, 1, 0):
-        pytest.skip()
     igh = ccrs.InterruptedGoodeHomolosine(
         central_longitude=lon, emphasis=emphasis
     )
diff --git a/lib/cartopy/tests/crs/test_orthographic.py b/lib/cartopy/tests/crs/test_orthographic.py
index d005a570b..0b4c1254b 100644
--- a/lib/cartopy/tests/crs/test_orthographic.py
+++ b/lib/cartopy/tests/crs/test_orthographic.py
@@ -43,9 +43,7 @@ def test_ellipse_globe():
     with pytest.warns(UserWarning,
                       match='does not handle elliptical globes.') as w:
         ortho = ccrs.Orthographic(globe=globe)
-        assert len(w) == (2
-                          if (5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0)
-                          else 1)
+        assert len(w) == 1
 
     other_args = {'ellps=WGS84', 'lon_0=0.0', 'lat_0=0.0'}
     check_proj_params('ortho', ortho, other_args)
@@ -61,9 +59,7 @@ def test_eccentric_globe():
     with pytest.warns(UserWarning,
                       match='does not handle elliptical globes.') as w:
         ortho = ccrs.Orthographic(globe=globe)
-        assert len(w) == (2
-                          if (5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0)
-                          else 1)
+        assert len(w) == 1
 
     other_args = {'a=1000', 'b=500', 'lon_0=0.0', 'lat_0=0.0'}
     check_proj_params('ortho', ortho, other_args)
diff --git a/lib/cartopy/tests/crs/test_robinson.py b/lib/cartopy/tests/crs/test_robinson.py
index d906da824..77f85624e 100644
--- a/lib/cartopy/tests/crs/test_robinson.py
+++ b/lib/cartopy/tests/crs/test_robinson.py
@@ -19,25 +19,14 @@
 _CRS_PC = ccrs.PlateCarree()
 _CRS_ROB = ccrs.Robinson()
 
-# Increase tolerance if using older proj releases
-if ccrs.PROJ_VERSION >= (6, 3, 1):
-    _TRANSFORM_TOL = 7
-elif ccrs.PROJ_VERSION >= (4, 9):
-    _TRANSFORM_TOL = 0
-else:
-    _TRANSFORM_TOL = -1
-_LIMIT_TOL = -1  # if ccrs.PROJ_VERSION < (5, 2, 0) else 7
-
 
 def test_default():
     robin = ccrs.Robinson()
     other_args = {'a=6378137.0', 'lon_0=0'}
     check_proj_params('robin', robin, other_args)
 
-    assert_almost_equal(robin.x_limits,
-                        [-17005833.3305252, 17005833.3305252])
-    assert_almost_equal(robin.y_limits,
-                        [-8625154.6651000, 8625154.6651000], _LIMIT_TOL)
+    assert_almost_equal(robin.x_limits, [-17005833.3305252, 17005833.3305252])
+    assert_almost_equal(robin.y_limits, [-8625154.6651000, 8625154.6651000])
 
 
 def test_sphere_globe():
@@ -47,8 +36,7 @@ def test_sphere_globe():
     check_proj_params('robin', robin, other_args)
 
     assert_almost_equal(robin.x_limits, [-2666.2696851, 2666.2696851])
-    assert_almost_equal(robin.y_limits, [-1352.3000000, 1352.3000000],
-                        _LIMIT_TOL)
+    assert_almost_equal(robin.y_limits, [-1352.3000000, 1352.3000000])
 
 
 def test_ellipse_globe():
@@ -63,8 +51,7 @@ def test_ellipse_globe():
 
     # Limits are the same as default since ellipses are not supported.
     assert_almost_equal(robin.x_limits, [-17005833.3305252, 17005833.3305252])
-    assert_almost_equal(robin.y_limits, [-8625154.6651000, 8625154.6651000],
-                        _LIMIT_TOL)
+    assert_almost_equal(robin.y_limits, [-8625154.6651000, 8625154.6651000])
 
 
 def test_eccentric_globe():
@@ -80,8 +67,7 @@ def test_eccentric_globe():
 
     # Limits are the same as spheres since ellipses are not supported.
     assert_almost_equal(robin.x_limits, [-2666.2696851, 2666.2696851])
-    assert_almost_equal(robin.y_limits, [-1352.3000000, 1352.3000000],
-                        _LIMIT_TOL)
+    assert_almost_equal(robin.y_limits, [-1352.3000000, 1352.3000000])
 
 
 def test_offset():
@@ -99,11 +85,9 @@ def test_central_longitude(lon):
     other_args = {'a=6378137.0', f'lon_0={lon}'}
     check_proj_params('robin', robin, other_args)
 
-    assert_almost_equal(robin.x_limits,
-                        [-17005833.3305252, 17005833.3305252],
+    assert_almost_equal(robin.x_limits, [-17005833.3305252, 17005833.3305252],
                         decimal=5)
-    assert_almost_equal(robin.y_limits,
-                        [-8625154.6651000, 8625154.6651000], _LIMIT_TOL)
+    assert_almost_equal(robin.y_limits, [-8625154.6651000, 8625154.6651000])
 
 
 def test_transform_point():
@@ -115,8 +99,7 @@ def test_transform_point():
 
     # this way has always worked
     result = _CRS_ROB.transform_point(35.0, 70.0, _CRS_PC)
-    assert_array_almost_equal(result, (2376187.2182271, 7275318.1162980),
-                              _TRANSFORM_TOL)
+    assert_array_almost_equal(result, (2376187.2182271, 7275318.1162980))
 
     # this always did something, but result has altered
     result = _CRS_ROB.transform_point(np.nan, 70.0, _CRS_PC)
@@ -139,16 +122,14 @@ def test_transform_points():
                                        np.array([35.0]),
                                        np.array([70.0]))
     assert_array_almost_equal(result,
-                              [[2376187.2182271, 7275318.1162980, 0]],
-                              _TRANSFORM_TOL)
+                              [[2376187.2182271, 7275318.1162980, 0]])
 
     result = _CRS_ROB.transform_points(_CRS_PC,
                                        np.array([35.0]),
                                        np.array([70.0]),
                                        np.array([0.0]))
     assert_array_almost_equal(result,
-                              [[2376187.2182271, 7275318.1162980, 0]],
-                              _TRANSFORM_TOL)
+                              [[2376187.2182271, 7275318.1162980, 0]])
 
     # this always did something, but result has altered
     result = _CRS_ROB.transform_points(_CRS_PC,
diff --git a/lib/cartopy/tests/crs/test_transverse_mercator.py b/lib/cartopy/tests/crs/test_transverse_mercator.py
index aef320cf3..ce4c56f67 100644
--- a/lib/cartopy/tests/crs/test_transverse_mercator.py
+++ b/lib/cartopy/tests/crs/test_transverse_mercator.py
@@ -92,9 +92,8 @@ def setup_class(self):
     def test_default(self, approx):
         proj = ccrs.OSNI(approx=approx)
         res = proj.transform_point(*self.point_a, src_crs=self.src_crs)
-        np.testing.assert_array_almost_equal(
-            res, (275614.26762651594, 386984.206429612),
-            decimal=0 if ccrs.PROJ_VERSION < (5, 0, 0) else 6)
+        np.testing.assert_array_almost_equal(res,
+                                             (275614.267627, 386984.206430))
 
     def test_nan(self):
         proj = ccrs.OSNI(approx=True)
diff --git a/lib/cartopy/tests/mpl/test_crs.py b/lib/cartopy/tests/mpl/test_crs.py
index 583c6e03b..c61ac83be 100644
--- a/lib/cartopy/tests/mpl/test_crs.py
+++ b/lib/cartopy/tests/mpl/test_crs.py
@@ -21,7 +21,6 @@ def test_igh_land():
     ax.gridlines()
 
 
-@pytest.mark.skipif(ccrs.PROJ_VERSION < (7, 1, 0), reason="Proj is too old.")
 @pytest.mark.natural_earth
 @ImageTesting(["igh_ocean"])
 def test_igh_ocean():
diff --git a/lib/cartopy/tests/mpl/test_gridliner.py b/lib/cartopy/tests/mpl/test_gridliner.py
index 9d14156ce..1bc9a950e 100644
--- a/lib/cartopy/tests/mpl/test_gridliner.py
+++ b/lib/cartopy/tests/mpl/test_gridliner.py
@@ -54,7 +54,7 @@
 @pytest.mark.natural_earth
 @ImageTesting(['gridliner1'],
               # Robinson projection is slightly better in Proj 6+.
-              tolerance=0.7 if ccrs.PROJ_VERSION >= (6, 0, 0) else 0.5)
+              tolerance=0.7)
 def test_gridliner():
     ny, nx = 2, 4
 
@@ -210,9 +210,7 @@ def test_grid_labels():
 
 @pytest.mark.skipif(geos_version == (3, 9, 0), reason="GEOS intersection bug")
 @pytest.mark.natural_earth
-@ImageTesting(['gridliner_labels_tight'],
-              tolerance=grid_label_tol if ccrs.PROJ_VERSION < (7, 1, 0)
-              else 4)
+@ImageTesting(['gridliner_labels_tight'], tolerance=4)
 def test_grid_labels_tight():
     # Ensure tight layout accounts for gridlines
     fig = plt.figure(figsize=(7, 5))
@@ -262,14 +260,7 @@ def test_grid_labels_inline():
         else:
             kwargs = {}
         ax = plt.subplot(7, 4, i, projection=proj(**kwargs))
-        if (ccrs.PROJ_VERSION[:2] == (5, 0) and
-                proj in (ccrs.Orthographic, ccrs.AlbersEqualArea,
-                         ccrs.Geostationary, ccrs.NearsidePerspective)):
-            # Above projections are broken, so skip labels.
-            # Add gridlines anyway to minimize image differences.
-            ax.gridlines()
-        else:
-            ax.gridlines(draw_labels=True, auto_inline=True)
+        ax.gridlines(draw_labels=True, auto_inline=True)
         ax.coastlines(resolution="110m")
         ax.set_title(proj, y=1.075)
     plt.subplots_adjust(wspace=0.35, hspace=0.35)
@@ -297,14 +288,7 @@ def test_grid_labels_inline_usa():
         except Exception:
             pass
         ax.set_title(proj, y=1.075)
-        if (ccrs.PROJ_VERSION[:2] == (5, 0) and
-                proj in (ccrs.Orthographic, ccrs.AlbersEqualArea,
-                         ccrs.Geostationary, ccrs.NearsidePerspective)):
-            # Above projections are broken, so skip labels.
-            # Add gridlines anyway to minimize image differences.
-            ax.gridlines()
-        else:
-            ax.gridlines(draw_labels=True, auto_inline=True, clip_on=True)
+        ax.gridlines(draw_labels=True, auto_inline=True, clip_on=True)
         ax.coastlines(resolution="110m")
 
     plt.subplots_adjust(wspace=0.35, hspace=0.35)
diff --git a/lib/cartopy/tests/mpl/test_images.py b/lib/cartopy/tests/mpl/test_images.py
index 0ba8ad229..8fc41a144 100644
--- a/lib/cartopy/tests/mpl/test_images.py
+++ b/lib/cartopy/tests/mpl/test_images.py
@@ -35,9 +35,6 @@
 # care that it is putting images onto the map which are roughly correct.
 @pytest.mark.natural_earth
 @pytest.mark.network
-@pytest.mark.xfail(ccrs.PROJ_VERSION == (5, 0, 0),
-                   reason='Proj returns slightly different bounds.',
-                   strict=True)
 @ImageTesting(['web_tiles'], tolerance=5.91)
 def test_web_tiles():
     extent = [-15, 0.1, 50, 60]
@@ -74,9 +71,6 @@ def test_web_tiles():
 
 @pytest.mark.natural_earth
 @pytest.mark.network
-@pytest.mark.xfail(ccrs.PROJ_VERSION == (5, 0, 0),
-                   reason='Proj returns slightly different bounds.',
-                   strict=True)
 @ImageTesting(['image_merge'], tolerance=0.01)
 def test_image_merge():
     # tests the basic image merging functionality
@@ -103,9 +97,6 @@ def test_image_merge():
     plt.imshow(img, origin=origin, extent=extent, alpha=0.5)
 
 
-@pytest.mark.xfail((5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0),
-                   reason='Proj Orthographic projection is buggy.',
-                   strict=True)
 @ImageTesting(['imshow_natural_earth_ortho'], tolerance=0.7)
 def test_imshow():
     source_proj = ccrs.PlateCarree()
@@ -170,18 +161,12 @@ def test_imshow_rgb():
     plt.close()
 
 
-@pytest.mark.xfail((5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0),
-                   reason='Proj Orthographic projection is buggy.',
-                   strict=True)
 @ImageTesting(['imshow_natural_earth_ortho'], tolerance=0.7)
 def test_stock_img():
     ax = plt.axes(projection=ccrs.Orthographic())
     ax.stock_img()
 
 
-@pytest.mark.xfail((5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0),
-                   reason='Proj Orthographic projection is buggy.',
-                   strict=True)
 @ImageTesting(['imshow_natural_earth_ortho'], tolerance=0.7)
 def test_pil_Image():
     img = Image.open(NATURAL_EARTH_IMG)
@@ -191,9 +176,6 @@ def test_pil_Image():
               extent=[-180, 180, -90, 90])
 
 
-@pytest.mark.xfail((5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0),
-                   reason='Proj Orthographic projection is buggy.',
-                   strict=True)
 @ImageTesting(['imshow_natural_earth_ortho'])
 def test_background_img():
     ax = plt.axes(projection=ccrs.Orthographic())
diff --git a/lib/cartopy/tests/mpl/test_mpl_integration.py b/lib/cartopy/tests/mpl/test_mpl_integration.py
index 3fdf9097f..79c5bbca0 100644
--- a/lib/cartopy/tests/mpl/test_mpl_integration.py
+++ b/lib/cartopy/tests/mpl/test_mpl_integration.py
@@ -211,8 +211,6 @@ def test_multiple_projections():
                  transform=prj.as_geodetic())
 
 
-@pytest.mark.skipif(ccrs.PROJ_VERSION < (5, 2, 0),
-                    reason='Proj is too old.')
 @pytest.mark.natural_earth
 @ImageTesting(['multiple_projections520'], tolerance=0.65)
 def test_multiple_projections_520():
@@ -345,15 +343,8 @@ def test_pcolormesh_get_array_with_mask():
         'Data supplied does not match data retrieved in unwrapped case'
 
 
-tolerance = 1.87
-if (5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0):
-    tolerance += 0.8
-
-
 @pytest.mark.natural_earth
-@ImageTesting(
-    ['pcolormesh_global_wrap2'],
-    tolerance=tolerance)
+@ImageTesting(['pcolormesh_global_wrap2'], tolerance=1.87)
 def test_pcolormesh_global_with_wrap2():
     # make up some realistic data with bounds (such as data from the UM)
     nx, ny = 36, 18
@@ -381,15 +372,8 @@ def test_pcolormesh_global_with_wrap2():
     ax.set_global()  # make sure everything is visible
 
 
-tolerance = 1.42
-if (5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0):
-    tolerance += 1.4
-
-
 @pytest.mark.natural_earth
-@ImageTesting(
-    ['pcolormesh_global_wrap3'],
-    tolerance=tolerance)
+@ImageTesting(['pcolormesh_global_wrap3'], tolerance=1.42)
 def test_pcolormesh_global_with_wrap3():
     nx, ny = 33, 17
     xbnds = np.linspace(-1.875, 358.125, nx, endpoint=True)
@@ -430,7 +414,7 @@ def test_pcolormesh_global_with_wrap3():
 
 
 @pytest.mark.natural_earth
-@ImageTesting(['pcolormesh_global_wrap3'], tolerance=tolerance)
+@ImageTesting(['pcolormesh_global_wrap3'], tolerance=1.42)
 def test_pcolormesh_set_array_with_mask():
     """Testing that set_array works with masked arrays properly."""
     nx, ny = 33, 17
@@ -480,7 +464,7 @@ def test_pcolormesh_set_array_with_mask():
 
 
 @pytest.mark.natural_earth
-@ImageTesting(['pcolormesh_global_wrap3'], tolerance=tolerance)
+@ImageTesting(['pcolormesh_global_wrap3'], tolerance=1.42)
 def test_pcolormesh_set_clim_with_mask():
     """Testing that set_clim works with masked arrays properly."""
     nx, ny = 33, 17
diff --git a/lib/cartopy/tests/mpl/test_web_services.py b/lib/cartopy/tests/mpl/test_web_services.py
index aff0f0180..1d4bfd3f4 100644
--- a/lib/cartopy/tests/mpl/test_web_services.py
+++ b/lib/cartopy/tests/mpl/test_web_services.py
@@ -37,9 +37,6 @@ def test_wms_tight_layout():
 
 
 @pytest.mark.network
-@pytest.mark.xfail((5, 0, 0) <= ccrs.PROJ_VERSION < (5, 1, 0),
-                   reason='Proj Orthographic projection is buggy.',
-                   strict=True)
 @pytest.mark.skipif(not _OWSLIB_AVAILABLE, reason='OWSLib is unavailable.')
 @ImageTesting(['wms'], tolerance=0.02)
 def test_wms():
diff --git a/lib/cartopy/tests/test_crs.py b/lib/cartopy/tests/test_crs.py
index 8871816e9..25bf934f0 100644
--- a/lib/cartopy/tests/test_crs.py
+++ b/lib/cartopy/tests/test_crs.py
@@ -75,18 +75,9 @@ def test_osgb(self, approx):
     def test_epsg(self):
         uk = ccrs.epsg(27700)
         assert uk.epsg_code == 27700
-        if ccrs.PROJ_VERSION >= (8, 0, 0):
-            assert_almost_equal(uk.x_limits, (-104009.357,  688806.007),
-                                decimal=3)
-            assert_almost_equal(uk.y_limits, (-8908.37, 1256558.45),
-                                decimal=2)
-            assert_almost_equal(uk.threshold, 7928.15, decimal=2)
-        else:
-            assert_almost_equal(uk.x_limits, (-118397.001,  751441.779),
-                                decimal=3)
-            assert_almost_equal(uk.y_limits, (-5192.07, 1272149.35),
-                                decimal=2)
-            assert_almost_equal(uk.threshold, 8698.39, decimal=2)
+        assert_almost_equal(uk.x_limits, (-104009.357,  688806.007), decimal=3)
+        assert_almost_equal(uk.y_limits, (-8908.37, 1256558.45), decimal=2)
+        assert_almost_equal(uk.threshold, 7928.15, decimal=2)
         self._check_osgb(uk)
 
     def test_epsg_compound_crs(self):
diff --git a/lib/cartopy/tests/test_img_tiles.py b/lib/cartopy/tests/test_img_tiles.py
index 7d7bea5ac..abe11a483 100644
--- a/lib/cartopy/tests/test_img_tiles.py
+++ b/lib/cartopy/tests/test_img_tiles.py
@@ -31,19 +31,6 @@
                  (8, 9, 4): (0, 2504688.542848654,
                              -5009377.085697312, -2504688.542848654),
                  }
-if ccrs.PROJ_VERSION == (5, 0, 0):
-    KNOWN_EXTENTS = {
-        (0, 0, 0): (-20037508.342789244, 20037508.342789244,
-                    -19994827.892149, 19994827.892149),
-        (2, 0, 2): (0, 10018754.171395,
-                    9997413.946075, 19994827.892149),
-        (0, 2, 2): (-20037508.342789244, -10018754.171394622,
-                    -9997413.946075, 0),
-        (2, 2, 2): (0, 10018754.171395,
-                    -9997413.946075, 0),
-        (8, 9, 4): (0, 2504688.542849,
-                    -4998706.973037, -2499353.486519),
-    }
 
 
 def GOOGLE_IMAGE_URL_REPLACEMENT(self, tile):
@@ -157,14 +144,9 @@ def test_image_for_domain():
     ll_extent = ccrs.Geodetic().transform_points(gt.crs,
                                                  np.array(extent[:2]),
                                                  np.array(extent[2:]))
-    if ccrs.PROJ_VERSION == (5, 0, 0):
-        assert_arr_almost(ll_extent[:, :2],
-                          [[-11.25, 49.033955],
-                           [11.25, 61.687101]])
-    else:
-        assert_arr_almost(ll_extent[:, :2],
-                          [[-11.25, 48.92249926],
-                           [11.25, 61.60639637]])
+    assert_arr_almost(ll_extent[:, :2],
+                      [[-11.25, 48.92249926],
+                       [11.25, 61.60639637]])
 
 
 def test_quadtree_wts():
diff --git a/lib/cartopy/trace.pyx b/lib/cartopy/trace.pyx
index 1d016a019..82ea1a431 100644
--- a/lib/cartopy/trace.pyx
+++ b/lib/cartopy/trace.pyx
@@ -589,18 +589,6 @@ def _interpolator(src_crs, dest_projection):
     else:
         interpolator = CartesianInterpolator()
     interpolator.init(src_crs, dest_projection)
-    if (6, 1, 1) <= PROJ_VERSION < (6, 3, 0):
-        # Workaround bug in Proj 6.1.1+ with +to_meter on +proj=ob_tran.
-        # See https://github.com/OSGeo/proj#1782.
-        lonlat = ('latlon', 'latlong', 'lonlat', 'longlat')
-        if (src_crs.proj4_params.get('proj', '') == 'ob_tran' and
-                src_crs.proj4_params.get('o_proj', '') in lonlat and
-                'to_meter' in src_crs.proj4_params):
-            interpolator.src_scale = src_crs.proj4_params['to_meter']
-        if (dest_projection.proj4_params.get('proj', '') == 'ob_tran' and
-                dest_projection.proj4_params.get('o_proj', '') in lonlat and
-                'to_meter' in dest_projection.proj4_params):
-            interpolator.dest_scale = 1 / dest_projection.proj4_params['to_meter']
     return interpolator
 
 
diff --git a/setup.py b/setup.py
index 21963de72..c04029448 100644
--- a/setup.py
+++ b/setup.py
@@ -62,7 +62,7 @@
 
 # Please keep in sync with INSTALL file.
 GEOS_MIN_VERSION = (3, 7, 2)
-PROJ_MIN_VERSION = (4, 9, 0)
+PROJ_MIN_VERSION = (8, 0, 0)
 
 
 def file_walk_relative(top, remove=''):
@@ -172,18 +172,6 @@ def find_proj_version_by_program(conda=None):
     return proj_version
 
 
-def get_proj_libraries():
-    """
-    This function gets the PROJ libraries to cythonize with
-    """
-    proj_libraries = ["proj"]
-    if os.name == "nt" and (6, 0, 0) <= proj_version < (6, 3, 0):
-        proj_libraries = [
-            "proj_{}_{}".format(proj_version[0], proj_version[1])
-        ]
-    return proj_libraries
-
-
 conda = os.getenv('CONDA_DEFAULT_ENV')
 if conda is not None and conda in sys.prefix:
     # Conda does not provide pkg-config compatibility, but the search paths
@@ -199,7 +187,7 @@ def get_proj_libraries():
         exit(1)
 
     proj_includes = []
-    proj_libraries = get_proj_libraries()
+    proj_libraries = ["proj"]
     proj_library_dirs = []
 
 else:
@@ -222,7 +210,7 @@ def get_proj_libraries():
             exit(1)
 
         proj_includes = []
-        proj_libraries = get_proj_libraries()
+        proj_libraries = ["proj"]
         proj_library_dirs = []
     else:
         if proj_version < PROJ_MIN_VERSION: