diff --git a/Project.toml b/Project.toml
index 0b4e563944f..23fa573b751 100644
--- a/Project.toml
+++ b/Project.toml
@@ -22,7 +22,7 @@ Calculus = "0.5"
 DataStructures = "0.18"
 ForwardDiff = "~0.5.0, ~0.6, ~0.7, ~0.8, ~0.9, ~0.10"
 JSON = "0.21"
-MathOptInterface = "~0.9.14"
+MathOptInterface = "~0.9.19"
 MutableArithmetics = "0.2"
 NaNMath = "0.3"
 SpecialFunctions = "0.8, 1"
diff --git a/docs/Project.toml b/docs/Project.toml
index 3f7711438a4..333ef4c0e57 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -11,7 +11,7 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
 Documenter = "~0.25"
-GLPK = "0.14"
+GLPK = "0.14.4"
 Ipopt = "0.6"
 MathOptInterface = "~0.9"
 SCS = "0.7"
diff --git a/docs/src/callbacks.md b/docs/src/callbacks.md
index baaa536218a..0d69041292e 100644
--- a/docs/src/callbacks.md
+++ b/docs/src/callbacks.md
@@ -40,23 +40,26 @@ Callback support is limited to a few solvers. This includes
 
 ## Things you can and cannot do during callbacks
 
-There is a very limited range of things you can do during a callback. Only use 
+There is a very limited range of things you can do during a callback. Only use
 the functions and macros explicitly stated in this page of the documentation, or
 in the [Callbacks example](/examples/callbacks).
 
 Using any other part of the JuMP API (e.g., adding a constraint with [`@constraint`](@ref)
 or modifying a variable bound with [`set_lower_bound`](@ref)) is undefined
-behavior, and your solver may throw an error, return an incorrect solution, or 
+behavior, and your solver may throw an error, return an incorrect solution, or
 result in a segfault that aborts Julia.
 
-In each of the three solver-independent callbacks, the only thing you may query is 
-the primal value of the variables using [`callback_value`](@ref).
+In each of the three solver-independent callbacks, there are two things you may
+query:
+ - [`callback_node_status`](@ref) returns an [`MOI.CallbackNodeStatusCode`](@ref)
+   enum indicating if the current primal solution is integer feasible.
+ - [`callback_value`](@ref) returns the current primal solution of a variable.
 
-If you need to query any other information, use a solver-dependent callback 
-instead. Each solver supporting a solver-dependent callback has information on 
+If you need to query any other information, use a solver-dependent callback
+instead. Each solver supporting a solver-dependent callback has information on
 how to use it in the README of their Github repository.
 
-If you want to modify the problem in a callback, you _must_ use a lazy 
+If you want to modify the problem in a callback, you _must_ use a lazy
 constraint.
 
 ## Lazy constraints
@@ -75,6 +78,18 @@ model = Model(GLPK.Optimizer)
 @variable(model, x <= 10, Int)
 @objective(model, Max, x)
 function my_callback_function(cb_data)
+    status = callback_node_status(cb_data, model)
+    if status == MOI.CALLBACK_NODE_STATUS_FRACTIONAL
+        # `callback_value(cb_data, x)` is not integer (to some tolerance).
+        # If, for example, your lazy constraint generator requires an
+        # integer-feasible primal solution, you can add a `return` here.
+        return
+    elseif status == MOI.CALLBACK_NODE_STATUS_INTEGER
+        # `callback_value(cb_data, x)` is integer (to some tolerance).
+    else
+        @assert status == MOI.CALLBACK_NODE_STATUS_UNKNOWN
+        # `callback_value(cb_data, x)` might be fractional or integer.
+    end
     x_val = callback_value(cb_data, x)
     if x_val > 2 + 1e-6
         con = @build_constraint(x <= 2)
@@ -88,11 +103,11 @@ MOI.set(model, MOI.LazyConstraintCallback(), my_callback_function)
     The lazy constraint callback _may_ be called at fractional or integer
     nodes in the branch-and-bound tree. There is no guarantee that the
     callback is called at _every_ primal solution.
-    
+
 !!! warn
     Only add a lazy constraint if your primal solution violates the constraint.
-    Adding the lazy constraint irrespective of feasibility may result in the 
-    solver returning an incorrect solution, or lead to a large number of 
+    Adding the lazy constraint irrespective of feasibility may result in the
+    solver returning an incorrect solution, or lead to a large number of
     constraints being added, slowing down the solution process.
     ```julia
     model = Model(GLPK.Optimizer)
diff --git a/docs/src/examples/callbacks.jl b/docs/src/examples/callbacks.jl
index 8a2d5734bb7..7e0c244a3cd 100644
--- a/docs/src/examples/callbacks.jl
+++ b/docs/src/examples/callbacks.jl
@@ -27,6 +27,15 @@ function example_lazy_constraint()
         x_val = callback_value(cb_data, x)
         y_val = callback_value(cb_data, y)
         println("Called from (x, y) = ($x_val, $y_val)")
+        status = callback_node_status(cb_data, model)
+        if status == MOI.CALLBACK_NODE_STATUS_FRACTIONAL
+            println(" - Solution is integer infeasible!")
+        elseif status == MOI.CALLBACK_NODE_STATUS_INTEGER
+            println(" - Solution is integer feasible!")
+        else
+            @assert status == MOI.CALLBACK_NODE_STATUS_UNKNOWN
+            println(" - I don't know if the solution is integer feasible :(")
+        end
         if y_val - x_val > 1 + 1e-6
             con = @build_constraint(y - x <= 1)
             println("Adding $(con)")
diff --git a/docs/src/reference/callbacks.md b/docs/src/reference/callbacks.md
index 399c3493301..f0929be7e70 100644
--- a/docs/src/reference/callbacks.md
+++ b/docs/src/reference/callbacks.md
@@ -5,5 +5,6 @@ of the manual.
 
 ```@docs
 @build_constraint
+callback_node_status
 callback_value
 ```
diff --git a/docs/src/reference/moi.md b/docs/src/reference/moi.md
new file mode 100644
index 00000000000..b0d3fc7fcd9
--- /dev/null
+++ b/docs/src/reference/moi.md
@@ -0,0 +1,12 @@
+# MathOptInterface API
+
+This page contains extracts from the `MathOptInterface` documentation. More
+information can be found at in the [MathOptInterface documentation](https://jump.dev/MathOptInterface.jl/stable/).
+
+```@docs
+MOI.CallbackNodeStatus
+MOI.CallbackNodeStatusCode
+MOI.CallbackVariablePrimal
+
+MOI.get
+```
diff --git a/src/callbacks.jl b/src/callbacks.jl
index f5bb8355f54..2dce4060817 100644
--- a/src/callbacks.jl
+++ b/src/callbacks.jl
@@ -8,6 +8,25 @@
 # See https://github.com/jump-dev/JuMP.jl
 #############################################################################
 
+"""
+    callback_node_status(cb_data, model::Model)
+
+Return an [`MOI.CallbackNodeStatusCode`](@ref) enum, indicating if the current
+primal solution available from [`callback_value`](@ref) is integer feasible.
+"""
+function callback_node_status(cb_data, model::Model)
+    # TODO(odow):
+    # MOI defines `is_set_by_optimize(::CallbackNodeStatus) = true`.
+    # This causes problems for JuMP because it checks the termination_status to
+    # see if optimize! has been called. Solutions are:
+    # 1) defining is_set_by_optimize = false
+    # 2) adding a flag to JuMP to store whether it is in a callback
+    # 3) adding IN_OPTIMIZE to termination_status for callbacks
+    # Once this is resolved, we can replace the current function with:
+    #     MOI.get(model, MOI.CallbackNodeStatus(cb_data))
+    return MOI.get(backend(model), MOI.CallbackNodeStatus(cb_data))
+end
+
 """
     callback_value(cb_data, x::VariableRef)
 
diff --git a/test/callbacks.jl b/test/callbacks.jl
index 22fdd066669..a7303e66c45 100644
--- a/test/callbacks.jl
+++ b/test/callbacks.jl
@@ -85,3 +85,18 @@ end
     quad_expr = expr^2
     @test callback_value(cb, quad_expr) == 4
 end
+
+@testset "callback_node_status" begin
+    mock = MOI.Utilities.MockOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    )
+    cb = DummyCallbackData()
+    model = direct_model(mock)
+    @variable(model, 0 <= x <= 2.5, Int)
+    MOIU.set_mock_optimize!(mock, mock -> begin
+        MOI.set(mock, MOI.TerminationStatus(), MOI.OPTIMAL)
+        MOI.set(mock, MOI.CallbackNodeStatus(cb), MOI.CALLBACK_NODE_STATUS_INTEGER)
+    end)
+    optimize!(model)
+    @test callback_node_status(cb, model) == MOI.CALLBACK_NODE_STATUS_INTEGER
+end