diff --git a/NEWS.md b/NEWS.md
index 0c12a86faac3d..087e30ae5ef1f 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -290,6 +290,12 @@ This section lists changes that do not have deprecation warnings.
     Its return value has been removed. Use the `process_running` function
     to determine if a process has already exited.
 
+  * The `RevString` type has been removed from the language; `reverse(::String)` returns
+    a `String` with code points (or fragments thereof) in reverse order. In general,
+    `reverse(s)` should return a string of the same type and encoding as `s` with code
+    points in reverse order; any string type that does so much override the `reverseind`
+    function to correctly compute reversed indices into the string type it returns.
+
 Library improvements
 --------------------
 
@@ -392,6 +398,11 @@ Library improvements
     The generic definition is constant time but calls `endof(s)` which may be inefficient.
     Therefore custom string types may want to define direct `ncodeunits` methods.
 
+  * `reverseind(s::AbstractString, i::Integer)` now has an efficient generic fallback, so
+    custom string types do not need to provide their own efficient defintions. The generic
+    definition relies on `ncodeunits` however, so for optimal performance you may need to
+    define a custom method for that function.
+
 Compiler/Runtime improvements
 -----------------------------
 
diff --git a/base/exports.jl b/base/exports.jl
index 2eec4350fcaf2..1497f597740f9 100644
--- a/base/exports.jl
+++ b/base/exports.jl
@@ -88,7 +88,6 @@ export
     Rational,
     Regex,
     RegexMatch,
-    RevString,
     RoundFromZero,
     RoundDown,
     RoundingMode,
diff --git a/base/precompile.jl b/base/precompile.jl
index b047275fbd82f..2e290813b5368 100644
--- a/base/precompile.jl
+++ b/base/precompile.jl
@@ -581,9 +581,6 @@ precompile(Tuple{typeof(Base.LineEdit.complete_line), Base.LineEdit.PromptState,
 precompile(Tuple{typeof(Base.LineEdit.input_string_newlines_aftercursor), Base.LineEdit.PromptState})
 precompile(Tuple{typeof(Base.LineEdit.complete_line), Base.REPL.REPLCompletionProvider, Base.LineEdit.PromptState})
 precompile(Tuple{getfield(Base, Symbol("#kw##parse")), Array{Any, 1}, typeof(Base.parse), String})
-precompile(Tuple{typeof(Base.isvalid), Base.RevString{String}, Int64})
-precompile(Tuple{typeof(Base.nextind), Base.RevString{String}, Int64})
-precompile(Tuple{typeof(Base.search), Base.RevString{String}, Array{Char, 1}, Int64})
 precompile(Tuple{typeof(Base.rsearch), String, Array{Char, 1}, Int64})
 precompile(Tuple{getfield(Base.REPLCompletions, Symbol("#kw##find_start_brace")), Array{Any, 1}, typeof(Base.REPLCompletions.find_start_brace), String})
 precompile(Tuple{typeof(Core.Inference.isbits), Tuple{Void, Void, Void}})
diff --git a/base/repl/REPLCompletions.jl b/base/repl/REPLCompletions.jl
index 2040476af8947..3e5056d613f26 100644
--- a/base/repl/REPLCompletions.jl
+++ b/base/repl/REPLCompletions.jl
@@ -225,7 +225,7 @@ end
 # closed start brace from the end of the string.
 function find_start_brace(s::AbstractString; c_start='(', c_end=')')
     braces = 0
-    r = RevString(s)
+    r = reverse(s)
     i = start(r)
     in_single_quotes = false
     in_double_quotes = false
@@ -259,7 +259,7 @@ function find_start_brace(s::AbstractString; c_start='(', c_end=')')
         braces == 1 && break
     end
     braces != 1 && return 0:-1, -1
-    method_name_end = reverseind(r, i)
+    method_name_end = reverseind(s, i)
     startind = nextind(s, rsearch(s, non_identifier_chars, method_name_end))
     return (startind:endof(s), method_name_end)
 end
diff --git a/base/shell.jl b/base/shell.jl
index b8923ced43d04..72ffd23d9a944 100644
--- a/base/shell.jl
+++ b/base/shell.jl
@@ -14,7 +14,7 @@ function shell_parse(str::AbstractString, interpolate::Bool=true;
                      special::AbstractString="")
     s = lstrip(str)
     # strips the end but respects the space when the string ends with "\\ "
-    r = RevString(s)
+    r = reverse(s)
     i = start(r)
     c_old = nothing
     while !done(r,i)
diff --git a/base/strings/search.jl b/base/strings/search.jl
index 23f813ea28b26..43e880a26b9e5 100644
--- a/base/strings/search.jl
+++ b/base/strings/search.jl
@@ -194,12 +194,6 @@ end
 search(s::AbstractString, t::AbstractString, i::Integer=start(s)) = _search(s, t, i)
 search(s::ByteArray, t::ByteArray, i::Integer=start(s)) = _search(s, t, i)
 
-function rsearch(s::AbstractString, c::Chars)
-    j = search(RevString(s), c)
-    j == 0 && return 0
-    endof(s)-j+1
-end
-
 """
     rsearch(s::AbstractString, chars::Chars, [start::Integer])
 
@@ -212,44 +206,50 @@ julia> rsearch("aaabbb","b")
 6:6
 ```
 """
-function rsearch(s::AbstractString, c::Chars, i::Integer)
-    e = endof(s)
-    j = search(RevString(s), c, e-i+1)
-    j == 0 && return 0
-    e-j+1
+function rsearch(s::AbstractString, c::Chars, i::Integer=start(s))
+    if i < 1
+        return i == 0 ? 0 : throw(BoundsError(s, i))
+    end
+    n = ncodeunits(s)
+    if i > n
+        return i == n+1 ? 0 : throw(BoundsError(s, i))
+    end
+    # r[reverseind(r,i)] == reverse(r)[i] == s[i]
+    # s[reverseind(s,j)] == reverse(s)[j] == r[j]
+    r = reverse(s)
+    j = search(r, c, reverseind(r, i))
+    j == 0 ? 0 : reverseind(s, j)
 end
 
 function _rsearchindex(s, t, i)
     if isempty(t)
-        return 1 <= i <= nextind(s,endof(s)) ? i :
+        return 1 <= i <= nextind(s, endof(s)) ? i :
                throw(BoundsError(s, i))
     end
-    t = RevString(t)
-    rs = RevString(s)
+    t = reverse(t)
+    rs = reverse(s)
     l = endof(s)
-    t1, j2 = next(t,start(t))
+    t1, j2 = next(t, start(t))
     while true
-        i = rsearch(s,t1,i)
-        if i == 0 return 0 end
-        c, ii = next(rs,l-i+1)
+        i = rsearch(s, t1, i)
+        i == 0 && return 0
+        c, ii = next(rs, reverseind(rs, i))
         j = j2; k = ii
         matched = true
-        while !done(t,j)
-            if done(rs,k)
+        while !done(t, j)
+            if done(rs, k)
                 matched = false
                 break
             end
-            c, k = next(rs,k)
-            d, j = next(t,j)
+            c, k = next(rs, k)
+            d, j = next(t, j)
             if c != d
                 matched = false
                 break
             end
         end
-        if matched
-            return nextind(s,l-k+1)
-        end
-        i = l-ii+1
+        matched && return nextind(s, reverseind(s, k))
+        i = reverseind(s, ii)
     end
 end
 
diff --git a/base/strings/string.jl b/base/strings/string.jl
index a7b152488faea..86c3cd82ca566 100644
--- a/base/strings/string.jl
+++ b/base/strings/string.jl
@@ -295,14 +295,6 @@ function first_utf8_byte(ch::Char)
     return b
 end
 
-function reverseind(s::String, i::Integer)
-    j = sizeof(s) + 1 - i
-    @inbounds while is_valid_continuation(codeunit(s, j))
-        j -= 1
-    end
-    return j
-end
-
 ## overload methods for efficiency ##
 
 isvalid(s::String, i::Integer) =
diff --git a/base/strings/strings.jl b/base/strings/strings.jl
index 0acad00f79ca7..1e442a09e406f 100644
--- a/base/strings/strings.jl
+++ b/base/strings/strings.jl
@@ -1,7 +1,7 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
 include("strings/errors.jl")
-include("strings/types.jl")
+include("strings/substring.jl")
 include("strings/basic.jl")
 include("strings/search.jl")
 include("strings/util.jl")
diff --git a/base/strings/types.jl b/base/strings/substring.jl
similarity index 78%
rename from base/strings/types.jl
rename to base/strings/substring.jl
index e4474e5cb7edc..38a2a57e333df 100644
--- a/base/strings/types.jl
+++ b/base/strings/substring.jl
@@ -1,9 +1,5 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
-# SubString and RevString types
-
-## substrings reference original strings ##
-
 """
     SubString(s::AbstractString, i::Integer, j::Integer=endof(s))
     SubString(s::AbstractString, r::UnitRange{<:Integer})
@@ -123,32 +119,13 @@ function unsafe_convert(::Type{Ptr{R}}, s::SubString{String}) where R<:Union{Int
     convert(Ptr{R}, pointer(s.string)) + s.offset
 end
 
-## reversed strings without data movement ##
-
-struct RevString{T<:AbstractString} <: AbstractString
-    string::T
-end
-
-endof(s::RevString) = endof(s.string)
-length(s::RevString) = length(s.string)
-sizeof(s::RevString) = sizeof(s.string)
-
-function next(s::RevString, i::Int)
-    n = endof(s); j = n-i+1
-    (s.string[j], n-prevind(s.string,j)+1)
-end
-
 """
-    reverse(s::AbstractString) -> AbstractString
-
-Reverses a string.
+    reverse(s::AbstractString) -> String
 
-Technically, this function reverses the codepoints in a string, and its
-main utility is for reversed-order string processing, especially for reversed
-regular-expression searches.  See also [`reverseind`](@ref) to convert indices
-in `s` to indices in `reverse(s)` and vice-versa, and [`graphemes`](@ref)
-to operate on user-visible "characters" (graphemes) rather than codepoints.
-See also [`Iterators.reverse`](@ref) for reverse-order iteration without making a copy.
+Reverses a string. Technically, this function reverses the codepoints in a string. See also
+[`reverseind`](@ref) to convert indices in `s` to indices in `reverse(s)` and vice-versa, and
+[`graphemes`](@ref) to operate on user-visible "characters" (graphemes) rather than codepoints. See
+also [`Iterators.reverse`](@ref) for reverse-order iteration without making a copy.
 
 # Examples
 ```jldoctest
@@ -162,10 +139,15 @@ julia> join(reverse(collect(graphemes("ax̂e")))) # reverses graphemes
 "ex̂a"
 ```
 """
-reverse(s::AbstractString) = RevString(s)
-reverse(s::RevString) = s.string
-
-## reverse an index i so that reverse(s)[i] == s[reverseind(s,i)]
+function reverse(s::AbstractString)::String
+    sprint() do io
+        i, j = start(s), endof(s)
+        while i ≤ j
+            c, j = s[j], prevind(s, j)
+            write(io, c)
+        end
+    end
+end
 
 """
     reverseind(v, i)
@@ -185,10 +167,7 @@ julia> for i in 1:length(r)
 Julia
 ```
 """
-reverseind(s::AbstractString, i) = chr2ind(s, length(s) + 1 - ind2chr(reverse(s), i))
-reverseind(s::RevString, i::Integer) = endof(s) - i + 1
-reverseind(s::SubString{String}, i::Integer) =
-    reverseind(s.string, nextind(s.string, endof(s.string))-s.offset-s.endof+i-1) - s.offset
+reverseind(s::AbstractString, i::Integer) = thisind(s, ncodeunits(s)-i+1)
 
 """
     repeat(s::AbstractString, r::Integer)
diff --git a/base/strings/util.jl b/base/strings/util.jl
index 0e556aa822ffe..dae171b36fef2 100644
--- a/base/strings/util.jl
+++ b/base/strings/util.jl
@@ -190,16 +190,15 @@ julia> rstrip(a)
 ```
 """
 function rstrip(s::AbstractString, chars::Chars=_default_delims)
-    r = RevString(s)
-    i = start(r)
-    while !done(r,i)
-        c, j = next(r,i)
-        if !(c in chars)
-            return SubString(s, 1, endof(s)-i+1)
-        end
+    a = start(s)
+    i = endof(s)
+    while a ≤ i
+        c = s[i]
+        j = prevind(s, i)
+        c in chars || return SubString(s, 1:i)
         i = j
     end
-    SubString(s, 1, 0)
+    SubString(s, a, a-1)
 end
 
 """
diff --git a/test/replcompletions.jl b/test/replcompletions.jl
index a45fb05c7d28e..9698b1622fdf9 100644
--- a/test/replcompletions.jl
+++ b/test/replcompletions.jl
@@ -3,7 +3,7 @@
 using Base.REPLCompletions
 
 let ex = quote
-        module CompletionFoo
+    module CompletionFoo
         mutable struct Test_y
             yy
         end
diff --git a/test/strings/types.jl b/test/strings/types.jl
index a9ce276c02961..12dd75a1bd421 100644
--- a/test/strings/types.jl
+++ b/test/strings/types.jl
@@ -1,6 +1,6 @@
 # This file is a part of Julia. License is MIT: https://julialang.org/license
 
-## SubString, RevString and Cstring tests ##
+## SubString and Cstring tests ##
 
 ## SubString tests ##
 u8str = "∀ ε > 0, ∃ δ > 0: |x-y| < δ ⇒ |f(x)-f(y)| < ε"
@@ -207,31 +207,13 @@ let s = "|η(α)-ϕ(κ)| < ε"
     @test length(SubString(s,4,11))==length(s[4:11])
 end
 
-## Reverse strings ##
-
-let rs = RevString("foobar")
-    @test length(rs) == 6
-    @test sizeof(rs) == 6
-    @test isascii(rs)
-end
-
-# issue #4586
-@test rsplit(RevString("ailuj"),'l') == ["ju","ia"]
-@test parse(Float64,RevString("64")) === 46.0
-
-# reverseind
-for T in (String, GenericString)
+@testset "reverseind" for T in (String, SubString, GenericString)
     for prefix in ("", "abcd", "\U0001d6a4\U0001d4c1", "\U0001d6a4\U0001d4c1c", " \U0001d6a4\U0001d4c1")
         for suffix in ("", "abcde", "\U0001d4c1β\U0001d6a4", "\U0001d4c1β\U0001d6a4c", " \U0001d4c1β\U0001d6a4")
             for c in ('X', 'δ', '\U0001d6a5')
                 s = convert(T, string(prefix, c, suffix))
                 r = reverse(s)
                 ri = search(r, c)
-                @test r == RevString(s)
-                @test c == s[reverseind(s, ri)] == r[ri]
-                s = RevString(s)
-                r = reverse(s)
-                ri = search(r, c)
                 @test c == s[reverseind(s, ri)] == r[ri]
                 s = convert(T, string(prefix, prefix, c, suffix, suffix))
                 pre = convert(T, prefix)
@@ -244,6 +226,18 @@ for T in (String, GenericString)
     end
 end
 
+@testset "reverseind of empty strings" begin
+    for s in ("",
+              SubString("", 1, 0),
+              SubString("ab", 1, 0),
+              SubString("ab", 2, 1),
+              SubString("ab", 3, 2),
+              GenericString(""))
+        @test reverseind(s, 0) == 1
+        @test reverseind(s, 1) == 0
+    end
+end
+
 ## Cstring tests ##
 
 # issue #13974: comparison against pointers