diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index a2a78a4..15ffdd8 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -19,7 +19,7 @@ jobs:
         arch:
           - x64
     steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
@@ -37,6 +37,6 @@ jobs:
       - uses: julia-actions/julia-buildpkg@v1
       - uses: julia-actions/julia-runtest@v1
       - uses: julia-actions/julia-processcoverage@v1
-      - uses: codecov/codecov-action@v1
+      - uses: codecov/codecov-action@v3
         with:
           file: lcov.info
diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
new file mode 100644
index 0000000..fadeeaa
--- /dev/null
+++ b/.github/workflows/docs.yml
@@ -0,0 +1,29 @@
+name: Documentation
+
+on:
+  push:
+    branches:
+      - 'master'
+    tags: '*'
+  pull_request:
+
+jobs:
+  build:
+    name: Documentation
+    permissions:
+      contents: write
+      statuses: write
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: 1.6
+      - uses: julia-actions/cache@v1
+      - name: Install dependencies
+        run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
+      - name: Build and deploy
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+          DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} # If authenticating with SSH deploy key
+        run: julia --project=docs/ docs/make.jl
diff --git a/.gitignore b/.gitignore
index 80516d7..95731a5 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,6 @@
-Manifest.toml
-.DS_Store
+*.jl.*.cov
+*.jl.cov
+*.jl.mem
+/Manifest.toml
+/docs/Manifest.toml
+/docs/build/
diff --git a/README.md b/README.md
index 6785f41..831fa3d 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,6 @@
 # CompositeTypes.jl
 
+[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://JuliaApproximation.github.io/CompositeTypes.jl/dev)
 [![Build Status](https://github.com/JuliaApproximation/CompositeTypes.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/CompositeTypes.jl/actions)
 [![Coverage Status](https://codecov.io/gh/JuliaApproximation/CompositeTypes.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaApproximation/CompositeTypes.jl)
 
diff --git a/docs/Project.toml b/docs/Project.toml
new file mode 100644
index 0000000..962d28c
--- /dev/null
+++ b/docs/Project.toml
@@ -0,0 +1,6 @@
+[deps]
+Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+CompositeTypes = "b152e2b5-7a66-4b01-a709-34e65c35f657"
+
+[compat]
+Documenter = "1.3"
diff --git a/docs/make.jl b/docs/make.jl
new file mode 100644
index 0000000..5bbc7af
--- /dev/null
+++ b/docs/make.jl
@@ -0,0 +1,30 @@
+using Documenter
+using CompositeTypes
+using CompositeTypes.Indexing
+using CompositeTypes.Display
+
+DocMeta.setdocmeta!(CompositeTypes, :DocTestSetup, :(using CompositeTypes); recursive=true)
+
+makedocs(;
+    modules=[CompositeTypes,CompositeTypes.Indexing,CompositeTypes.Display],
+    authors="Daan Huybrechs <daan.huybrechs@kuleuven.be> and contributors",
+    sitename="CompositeTypes.jl",
+    format=Documenter.HTML(;
+        edit_link="main",
+        assets=String[],
+    ),
+    pages=[
+        "Home" => "index.md",
+        "API" => Any[
+            "Public API Reference" => "api.md",
+            "Internal API Reference" => "internal.md"
+        ],
+        "Indexing submodule" => "indexing.md",
+        "Display submodule" => "display.md"
+    ],
+)
+
+deploydocs(
+    repo   = "github.com/JuliaApproximation/CompositeTypes.jl.git",
+    devbranch = "master"
+)
diff --git a/docs/src/api.md b/docs/src/api.md
new file mode 100644
index 0000000..02e7661
--- /dev/null
+++ b/docs/src/api.md
@@ -0,0 +1,31 @@
+# Public API Reference
+
+This is an exhaustive list of all exported constants, types and functions
+in `CompositeTypes.jl`.
+
+## Constants
+
+```@autodocs
+Modules = [CompositeTypes]
+Order   = [:constant]
+Public  = true
+Private = false
+```
+
+## Functions
+
+```@autodocs
+Modules = [CompositeTypes]
+Order   = [:function]
+Public  = true
+Private = false
+```
+
+## Types
+
+```@autodocs
+Modules = [CompositeTypes]
+Order   = [:type]
+Public  = true
+Private = false
+```
diff --git a/docs/src/display.md b/docs/src/display.md
new file mode 100644
index 0000000..61bcfc7
--- /dev/null
+++ b/docs/src/display.md
@@ -0,0 +1,70 @@
+# Display
+
+## Public API Reference
+
+This is an exhaustive list of all exported constants, types and functions
+in `CompositeTypes.Display`.
+
+### Constants
+
+```@autodocs
+Modules = [Display]
+Order   = [:constant]
+Public  = true
+Private = false
+```
+
+### Functions
+
+```@autodocs
+Modules = [Display]
+Order   = [:function]
+Public  = true
+Private = false
+```
+
+### Types
+
+```@autodocs
+Modules = [Display]
+Order   = [:type]
+Public  = true
+Private = false
+```
+
+
+## Internal API Reference
+
+This is an exhaustive list of all non-exported constants, types and functions
+in `CompositeTypes.Display`.
+
+!!! warning
+    Unexported functions and types are subject to change across different
+    releases of the package, even if the release is said to be non-breaking.
+
+### Constants
+
+```@autodocs
+Modules = [Display]
+Order   = [:constant]
+Public  = false
+Private = true
+```
+
+### Functions
+
+```@autodocs
+Modules = [Display]
+Order   = [:function]
+Public  = false
+Private = true
+```
+
+### Types
+
+```@autodocs
+Modules = [Display]
+Order   = [:type]
+Public  = false
+Private = true
+```
diff --git a/docs/src/index.md b/docs/src/index.md
new file mode 100644
index 0000000..794ac45
--- /dev/null
+++ b/docs/src/index.md
@@ -0,0 +1,92 @@
+# CompositeTypes.jl
+
+CompositeTypes.jl defines an interface for types that consist of multiple components.
+
+## Interface
+
+The package defines the following functions:
+```@docs; canonical=false
+iscomposite(x)
+components(x)
+component(x, I...)
+ncomponents(x)
+setcomponent!(x, v, I...)
+```
+
+A type can declare to be composite simply by implementing `components(x)`, and
+returning something with non-zero `length`.
+
+## Indexing
+
+The submodule `Indexing` defines a generic way to index components of a
+composite object. For example, using the `DomainSets.jl` package:
+```julia
+julia> using DomainSets, CompositeTypes.Indexing
+
+julia> d = UnitCube(3); components(d)
+3-element Vector{UnitInterval{Float64}}:
+ 0.0..1.0 (Unit)
+ 0.0..1.0 (Unit)
+ 0.0..1.0 (Unit)
+
+julia> d[Component(1)]
+ 0.0..1.0 (Unit)
+
+julia> d[Component(1):Component(2)]
+2-element Vector{UnitInterval{Float64}}:
+ 0.0..1.0 (Unit)
+ 0.0..1.0 (Unit)
+```
+
+## Display
+
+### Examples
+
+Composite types can opt-in to a structured multi-line representation by
+defining a display stencil and specializing `show`. An example, again using
+the `DomainSets.jl` package:
+```julia
+julia> using DomainSets
+
+julia> boundary(UnitCube(3))
+D₄ ∪ D₁ ∪ D₃
+
+D₁ = (0.0..1.0 (Unit)) × D₂ × (0.0..1.0 (Unit))
+D₂ = Point{Float64}(0.0) ∪ Point{Float64}(1.0)
+D₃ = (0.0..1.0 (Unit)) × (0.0..1.0 (Unit)) × D₂
+D₄ = D₂ × (0.0..1.0 (Unit)) × (0.0..1.0 (Unit))
+```
+The display routines recursively evaluate display stencils of all objects
+appearing in the stencil of an object, up to a maximum recursion depth. An
+attempt is made to define symbols, such that the output remains somewhat
+readable.
+
+Both the `ProductDomain` and `UnionDomain` types are composite types. They
+combine their components using a `combinationsymbol`, in this case `∪` and `×`.
+The output above is achieved with the definitions, for `ProductDomain`:
+```julia
+using CompositeTypes.Display
+Display.combinationsymbol(d::ProductDomain) = Display.Symbol('×')
+Display.displaystencil(d::ProductDomain) = composite_displaystencil(d)
+
+show(io::IO, mime::MIME"text/plain", d::ProductDomain) = composite_show(io, mime, d)
+show(io::IO, d::ProductDomain) = composite_show_compact(io, d)
+```
+The invocation of `show` with the `mime` argument indicates that a multi-line
+representation can be shown. The shorter `show(io, x)` function typically expects
+a one-line representation. Types can choose to implement either function. Typically
+the longer version is the most useful, while for the compact version it may be
+safer to rely on Julia's default.
+
+A type can define a custom display stencil, which is a vector in which each string
+or character ends up being displayed, and each object is replaced by its own
+display stencil or by a compact string representation. For example:
+```julia
+Display.displaystencil(object::LinearMap) = [object.A, " * x + ", object.b]
+```
+
+### Relevant functions
+
+```@docs; canonical=false
+Display.displaystencil
+```
diff --git a/docs/src/indexing.md b/docs/src/indexing.md
new file mode 100644
index 0000000..1172d41
--- /dev/null
+++ b/docs/src/indexing.md
@@ -0,0 +1,70 @@
+# Indexing
+
+## Public API Reference
+
+This is an exhaustive list of all exported constants, types and functions
+in `CompositeTypes.Indexing`.
+
+### Constants
+
+```@autodocs
+Modules = [Indexing]
+Order   = [:constant]
+Public  = true
+Private = false
+```
+
+### Functions
+
+```@autodocs
+Modules = [Indexing]
+Order   = [:function]
+Public  = true
+Private = false
+```
+
+### Types
+
+```@autodocs
+Modules = [Indexing]
+Order   = [:type]
+Public  = true
+Private = false
+```
+
+
+## Internal API Reference
+
+This is an exhaustive list of all non-exported constants, types and functions
+in `CompositeTypes.Indexing`.
+
+!!! warning
+    Unexported functions and types are subject to change across different
+    releases of the package, even if the release is said to be non-breaking.
+
+### Constants
+
+```@autodocs
+Modules = [Indexing]
+Order   = [:constant]
+Public  = false
+Private = true
+```
+
+### Functions
+
+```@autodocs
+Modules = [Indexing]
+Order   = [:function]
+Public  = false
+Private = true
+```
+
+### Types
+
+```@autodocs
+Modules = [Indexing]
+Order   = [:type]
+Public  = false
+Private = true
+```
diff --git a/docs/src/internal.md b/docs/src/internal.md
new file mode 100644
index 0000000..78caee1
--- /dev/null
+++ b/docs/src/internal.md
@@ -0,0 +1,35 @@
+# Internal API Reference
+
+This is an exhaustive list of all non-exported constants, types and functions
+in `CompositeTypes.jl`.
+
+!!! warning
+    Unexported functions and types are subject to change across different
+    releases of the package, even if the release is said to be non-breaking.
+
+## Constants
+
+```@autodocs
+Modules = [CompositeTypes]
+Order   = [:constant]
+Public  = false
+Private = true
+```
+
+## Functions
+
+```@autodocs
+Modules = [CompositeTypes]
+Order   = [:function]
+Public  = false
+Private = true
+```
+
+## Types
+
+```@autodocs
+Modules = [CompositeTypes]
+Order   = [:type]
+Public  = false
+Private = true
+```
diff --git a/src/CompositeTypes.jl b/src/CompositeTypes.jl
index a393838..f314a3f 100644
--- a/src/CompositeTypes.jl
+++ b/src/CompositeTypes.jl
@@ -17,16 +17,24 @@ If an object is composite, then its components can be queried using the
 """
 iscomposite(x) = length(components(x)) > 0
 
-"Return the components of the composite object `x`."
+"""
+    components(x)
+
+The components of the composite object `x`.
+"""
 components(x) = ()
 
-"Return the number of components of composite object `x`."
+"""
+    ncomponents(x)
+
+The number of components of composite object `x`.
+"""
 ncomponents(x) = length(components(x))
 
 """
     component(x, I...)
 
-Return the component of `x` that corresponds to the given index.
+The component of `x` that corresponds to the given index.
 """
 component(x, I...) = getindex(components(x), I...)
 
diff --git a/src/Display.jl b/src/Display.jl
index 3d2cf78..889bfd8 100644
--- a/src/Display.jl
+++ b/src/Display.jl
@@ -97,6 +97,8 @@ end
 hasstencil(object) = length(displaystencil(object)) > 0
 
 """
+    displaystencil(object)
+
 Return the stencil of the object as an array.
 
 The stencil of an object determines how it is displayed. The array may
@@ -117,6 +119,8 @@ displaystencil(object) = []
 constructorname(object) = typename(object)
 
 """
+    composite_displaystencil(object; kwargs...)
+
 Default display stencil for composite objects.
 
 The default leads to the representation `typename(component1, components2, ...)`,
@@ -170,11 +174,17 @@ end
 SymbolObject(object) = SymbolObject(object, displaysymbol(object))
 displaysymbol(object::SymbolObject) = object.sym
 
-"Return all objects appearing in the display stencil."
+"""
+    stencil_objects(object)
+
+Return all objects appearing in the display stencil.
+"""
 stencil_objects(object) = objects(displaystencil(object))
 objects(A::Vector) = unique([el for el in A if !istext(el)])
 
 """
+    compact_repr(object)
+
 The conventional compact representation of an object.
 
 This representation is based on `show(io, d)`. If an object has overriden
@@ -212,7 +222,11 @@ function recursive_stencils(object, depth = 1, maxdepth = maximum_depth(object),
     stencils
 end
 
-"If an object in the stencil is complicated, should we put parentheses around it?"
+"""
+    stencil_parentheses(object)
+
+If an object in the stencil is complicated, should we put parentheses around it?
+"""
 function stencil_parentheses(object)
     if hasstencil(object)
         iscomposite(object) && !is_comma_separated(object)
@@ -221,7 +235,11 @@ function stencil_parentheses(object)
     end
 end
 
-"If this object appears in a more complicated expression, does it require parentheses?"
+"""
+    object_parentheses(object)
+
+If this object appears in a more complicated expression, does it require parentheses?
+"""
 function object_parentheses(object)
     if iscomposite(object)
         !is_comma_separated(object)
@@ -324,6 +342,8 @@ end
 
 
 """
+    composite_show(io::IO, ::MIME"text/plain", object)
+
 Display multi-line structured information about a composite object,
 using the stencil of the object and, recursively, the stencils of any objects
 therein.
@@ -368,6 +388,8 @@ function composite_show(io::IO, object)
 end
 
 """
+    composite_show_compact(io::IO, object)
+
 Display structured information about a composite object using its stencil,
 but not recursively.
 """
diff --git a/src/Indexing.jl b/src/Indexing.jl
index aedd7f3..1aaab51 100644
--- a/src/Indexing.jl
+++ b/src/Indexing.jl
@@ -5,7 +5,11 @@ export Component, ComponentIndex
 using ..CompositeTypes
 
 
-"Supertype of indices that select components of an object rather than its entries."
+"""
+    ComponentIndex{I}
+
+Supertype of indices that select components of an object rather than its entries.
+"""
 abstract type ComponentIndex{I} end
 
 import Base.(:)
@@ -29,6 +33,8 @@ function _iterate(idx::ComponentIndex, it)
 end
 
 """
+    Component{I}
+
 Component index of a composite type.
 
 Internally, this index simply stores an index or a range of indices to
@@ -38,10 +44,18 @@ struct Component{I} <: ComponentIndex{I}
     i   ::  I
 end
 
-"Create a new component index of the same type but with a different value."
+"""
+    similarindex(idx::Component, I)
+
+Create a new component index of the same type but with a different value.
+"""
 similarindex(idx::Component, I) = Component(I)
 
-"Convert the component index to an index of `components`."
+"""
+    to_index(idx::Component)
+
+Convert the component index to an index of `components`.
+"""
 to_index(idx::Component) = idx.i