diff --git a/src/atoms/IndexAtom.jl b/src/atoms/IndexAtom.jl
index e3b3d76ac..6c99f5679 100644
--- a/src/atoms/IndexAtom.jl
+++ b/src/atoms/IndexAtom.jl
@@ -114,10 +114,7 @@ function Base.getindex(x::AbstractExpr, I::AbstractVector{Bool})
 end
 
 # All rows and columns
-function Base.getindex(x::AbstractExpr, ::Colon, ::Colon)
-    rows, cols = size(x)
-    return getindex(x, 1:rows, 1:cols)
-end
+Base.getindex(x::AbstractExpr, ::Colon, ::Colon) = x
 
 # All rows for this column(s)
 function Base.getindex(x::AbstractExpr, ::Colon, col)
diff --git a/src/atoms/VcatAtom.jl b/src/atoms/VcatAtom.jl
index 3b6d34df3..3a1c20a15 100644
--- a/src/atoms/VcatAtom.jl
+++ b/src/atoms/VcatAtom.jl
@@ -59,3 +59,71 @@ function Base.vcat(args::Union{AbstractExpr,Value}...)
     end
     return VcatAtom(args...)
 end
+
+function Base.getindex(
+    x::VcatAtom,
+    rows::AbstractVector{<:Real},
+    cols::AbstractVector{<:Real},
+)
+    idx = 0
+    rows = collect(rows) # make a mutable copy
+    keep_children = ()
+    for c in x.children
+        # here are the row indices into `x` that point to `c`
+        I = idx .+ (1:size(c, 1))
+        if issubset(rows, I)
+            # if all the row indices we want are in this one child, we can early exit
+            if rows == I && cols == 1:size(c, 2)
+                return c
+            else
+                return c[rows.-idx, cols]
+            end
+        elseif !isdisjoint(rows, I)
+            # we have some but not all rows in this child, so keep it
+            keep_children = (keep_children..., c)
+            idx += size(c, 1)
+        else # we can drop this child!
+            # let's update `rows` to account for the removal
+            l = last(I)
+            for i in eachindex(rows)
+                if rows[i] >= l
+                    rows[i] -= length(I)
+                end
+            end
+        end
+    end
+    # If we are here, the indices span multiple children.
+    # We can't necessarily index each separately, since they may be out of order.
+    # So we will defer to an `IndexAtom` on the remaining children
+    remaining = VcatAtom(keep_children...)
+    return IndexAtom(remaining, rows, cols)
+end
+
+# linear indexing: very similar to row-indexing above, but with linear indices
+function Base.getindex(x::VcatAtom, inds::AbstractVector{<:Real})
+    idx = 0
+    inds = collect(inds)
+    keep_children = ()
+    for c in x.children
+        I = idx .+ (1:length(c))
+        if issubset(inds, I)
+            if inds == I
+                return c
+            else
+                return c[inds.-idx]
+            end
+        elseif !isdisjoint(inds, I)
+            keep_children = (keep_children..., c)
+            idx += length(c)
+        else
+            l = last(I)
+            for i in eachindex(inds)
+                if inds[i] >= l
+                    inds[i] -= length(I)
+                end
+            end
+        end
+    end
+    remaining = VcatAtom(keep_children...)
+    return IndexAtom(remaining, inds)
+end
diff --git a/test/test_atoms.jl b/test/test_atoms.jl
index dd2ab90be..2c373c74f 100644
--- a/test/test_atoms.jl
+++ b/test/test_atoms.jl
@@ -477,9 +477,8 @@ function test_IndexAtom()
     _test_atom(target) do context
         return Variable(2)[:, 1]
     end
-    _test_atom(target) do context
-        return Variable(2)[:, :]
-    end
+    x = Variable(2)
+    @test x[:, :] === x
     target = """
     variables: x1, x2, x3
     minobjective: [1.0 * x1, 1.0 * x3]
@@ -814,6 +813,42 @@ function test_VcatAtom()
     return
 end
 
+function test_VcatAtom_getindex()
+    x = Variable()
+    sq = square(x)
+    for v in [vcat(x, sq, -sq), vcat(vcat(x, sq), -sq)]
+        @test isequal(v[1], x)
+        @test isequal(v[2], sq)
+        @test isequal(v[:, 1], v[1:3, 1])
+        @test isequal(v[1:3, :], v[1:3, 1:1])
+        @test v[2:-1:1].children[1] isa Convex.VcatAtom
+        @test v[2:-1:1].children[1].children == (x, sq)
+        @test vexity(v[1]) isa Convex.AffineVexity
+        @test vexity(v[2]) isa Convex.ConvexVexity
+        @test vexity(v[3]) isa Convex.ConcaveVexity
+        @test vexity(v[1:2]) isa Convex.ConvexVexity
+        @test vexity(v[:, 1]) isa Convex.NotDcp
+    end
+    x = Variable(2, 2)
+    sq = square(x)
+    for v in [vcat(x, sq, -sq), vcat(vcat(x, sq), -sq)]
+        @test isequal(v[:, :], v)
+        @test isequal(v[1:2, 1:2], x)
+        @test v[1, 1:2] isa Convex.IndexAtom
+        @test v[1:3, 1:2] isa Convex.IndexAtom
+        @test v[1:3, 1:2].children[1] isa Convex.VcatAtom
+        @test isequal(v[3:4, 1:2], sq)
+        @test v[3:-1:1, 1].children[1] isa Convex.VcatAtom
+        @test v[4:-1:1, :].children[1].children == (x, sq)
+        @test vexity(v[1]) isa Convex.AffineVexity
+        @test vexity(v[3:4, 1:2]) isa Convex.ConvexVexity
+        @test vexity(v[5:6, 1]) isa Convex.ConcaveVexity
+        @test vexity(v[5:6, 1:2]) isa Convex.ConcaveVexity
+        @test vexity(v[1:3, 1]) isa Convex.ConvexVexity
+    end
+    return
+end
+
 ### exp_+_sdp_cone/LogDetAtom
 
 function test_LogDetAtom()