diff --git a/R/S3.R b/R/S3.R
index e399b1eb..dcfbe0ff 100644
--- a/R/S3.R
+++ b/R/S3.R
@@ -2,6 +2,7 @@
 #'
 #' To use an S3 class with S7, you must explicitly declare it using
 #' `new_S3_class()` because S3 lacks a formal class definition.
+#' (Unless it's an important base class already defined in [base_s3_classes].)
 #'
 #' # Method dispatch, properties, and unions
 #' There are three ways of using S3 with S7 that only require the S3 class
@@ -180,8 +181,19 @@ validate_data.frame <- function(self) {
   }
 }
 
+#' S7 wrappers for key S3 classes
+#'
+#' @description
+#' S7 bundles [S3 definitions][new_S3_class] for key S3 classes provided by
+#' the base package:
+#'
+#' * `class_data.frame` for data frames.
+#' * `class_Date` for dates.
+#' * `class_factor` for factors.
+#' * `class_POSIXct` for `POSIXct` date-times.
+#'
 #' @export
-#' @rdname base_classes
+#' @name base_s3_classes
 #' @format NULL
 #' @order 3
 class_factor <- new_S3_class("factor",
@@ -192,7 +204,7 @@ class_factor <- new_S3_class("factor",
 )
 
 #' @export
-#' @rdname base_classes
+#' @rdname base_s3_classes
 #' @format NULL
 #' @order 3
 class_Date <- new_S3_class("Date",
@@ -203,7 +215,7 @@ class_Date <- new_S3_class("Date",
 )
 
 #' @export
-#' @rdname base_classes
+#' @rdname base_s3_classes
 #' @format NULL
 #' @order 3
 class_POSIXct <- new_S3_class("POSIXct",
@@ -214,7 +226,7 @@ class_POSIXct <- new_S3_class("POSIXct",
 )
 
 #' @export
-#' @rdname base_classes
+#' @rdname base_s3_classes
 #' @format NULL
 #' @order 3
 class_data.frame <- new_S3_class("data.frame",
diff --git a/R/base.R b/R/base.R
index 729775c6..753da654 100644
--- a/R/base.R
+++ b/R/base.R
@@ -54,13 +54,11 @@ str.S7_base_class <- function(object, ..., nest.lev = 0) {
   print(object, ..., nest.lev = nest.lev)
 }
 
-#' Base classes
+#' S7 wrappers for base types
 #'
 #' @description
-#' These classes represent base types allowing them to be used within S7.
-#' There are three categories: base types, unions types, and key S3 classes.
-#'
-#' Base types:
+#' The following S7 classes represent base types allowing them to be used
+#' within S7:
 #'
 #' * `class_logical`
 #' * `class_integer`
@@ -73,7 +71,8 @@ str.S7_base_class <- function(object, ..., nest.lev = 0) {
 #' * `class_function`
 #' * `class_environment` (can only be used for properties)
 #'
-#' Union types:
+#' We also include three union types to model numerics, atomics, and vectors
+#' respectively:
 #'
 #' * `class_numeric` is a union of `class_integer` and `class_double`.
 #' * `class_atomic` is a union of `class_logical`, `class_numeric`,
@@ -81,13 +80,6 @@ str.S7_base_class <- function(object, ..., nest.lev = 0) {
 #' * `class_vector` is a union of `class_atomic`, `class_list`, and
 #'   `class_expression`.
 #'
-#' Key S3 classes:
-#'
-#' * `class_data.frame`
-#' * `class_Date`
-#' * `class_factor`
-#' * `class_POSIXct`
-#'
 #' @order 0
 #' @name base_classes
 #' @return S7 classes wrapping around common base types and S3 classes.
diff --git a/R/class-spec.R b/R/class-spec.R
index d3237383..525766f6 100644
--- a/R/class-spec.R
+++ b/R/class-spec.R
@@ -12,6 +12,7 @@
 #'   * A base class, like [class_logical], [class_integer], or [class_double].
 #'   * A "special", either [class_missing] or [class_any].
 #' @param arg Argument name used when generating errors.
+#' @keywords internal
 #' @export
 #' @return A standardised class: either `NULL`, an S7 class, an S7 union,
 #'   as [new_S3_class], or a S4 class.
diff --git a/R/method-introspect.R b/R/method-introspect.R
index fbaf6200..6011875f 100644
--- a/R/method-introspect.R
+++ b/R/method-introspect.R
@@ -1,14 +1,15 @@
-#' Retrieve a method for an S7 generic
+#' Find a method for an S7 generic
 #'
-#' `method()` takes a generic and signature and retrieves the corresponding
-#' method. This is rarely needed because most of the time you'll rely on the
-#' the generic, via [S7_dispatch()], to find and call the method for you.
-#' However, this introspection is useful if you want to see the implementation
-#' of a specific method.
+#' `method()` takes a generic and class signature and performs method dispatch
+#' to find the corresponding method implementation. This is rarely needed
+#' because you'll usually rely on the the generic to do dispatch for you (via
+#' [S7_dispatch()]). However, this introspection is useful if you want to see
+#' the implementation of a specific method.
 #'
 #' @seealso [method_explain()] to explain why a specific method was picked.
 #' @inheritParams method<-
-#' @returns A function with class <S7_method>.
+#' @returns Either a function with class `S7_method` or an error if no
+#'   matching method is found.
 #' @param class,object Perform introspection either with a `class`
 #'   (processed with [as_class()]) or a concrete `object`. If `generic` uses
 #'   multiple dispatch then both `object` and `class` must be a list of
diff --git a/R/method-register.R b/R/method-register.R
index ba0a535c..dbd22c0a 100644
--- a/R/method-register.R
+++ b/R/method-register.R
@@ -1,4 +1,4 @@
-#' Register a S7 method for a generic
+#' Register an S7 method for a generic
 #'
 #' @description
 #' A generic defines the interface of a function. Once you have created a
diff --git a/R/special.R b/R/special.R
index a812e6c1..1afbae03 100644
--- a/R/special.R
+++ b/R/special.R
@@ -1,20 +1,19 @@
-#' Special dispatch types
+#' Dispatch on a missing argument
 #'
-#' * Use `class_missing` when the user has not supplied an argument
-#' * Use `class_any` for a default method that is called only if no other
-#'   methods are matched
+#' Use `class_missing` to dispatch when the user has not supplied an argument,
+#' i.e. it's missing in the sense of [missing()], not in the sense of
+#' [is.na()].
 #'
 #' @export
 #' @return Sentinel objects used for special types of dispatch.
+#' @format NULL
 #' @examples
 #' foo <- new_generic("foo", "x")
-#' method(foo, class_integer) <- function(x) "integer"
-#' method(foo, class_missing) <- function(x) "missing"
+#' method(foo, class_numeric) <- function(x) "number"
 #' method(foo, class_any) <- function(x) "fallback"
 #'
 #' foo(1)
 #' foo()
-#' foo("x")
 class_missing <- structure(list(), class = "S7_missing")
 
 is_class_missing <- function(x) inherits(x, "S7_missing")
@@ -30,8 +29,20 @@ str.S7_missing <- function(object, ..., nest.lev = 0) {
   print(object)
 }
 
+#' Dispatch on any class
+#'
+#' Use `class_any` to register a default method that is called when no other
+#' methods are matched.
+#'
 #' @export
-#' @rdname class_missing
+#' @format NULL
+#' @examples
+#' foo <- new_generic("foo", "x")
+#' method(foo, class_numeric) <- function(x) "number"
+#' method(foo, class_any) <- function(x) "fallback"
+#'
+#' foo(1)
+#' foo("x")
 class_any <- structure(list(), class = "S7_any")
 
 is_class_any <- function(x) inherits(x, "S7_any")
diff --git a/_pkgdown.yml b/_pkgdown.yml
index 3a0e795e..9406eeef 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -24,17 +24,30 @@ reference:
 - title: Method dispatch
   contents:
   - convert
-  - super
-  - as_class
+  - class_missing
+  - class_any
   - method
   - method_explain
+  - super
+  - S7_class
+
+- title: Packages
+  desc: >
+    Functions needed when using S7 within a package. See `vignette("packages")`
+    for more details.
+  contents:
   - methods_register
   - new_external_generic
+
+- title: Compatibility
+  desc: >
+    These tools provide a layer of compatibility between S7 and S3 classes, S4
+    classes, and base types. See `vignette("compatibility")` for more details.
+  contents:
+  - base_classes
+  - base_s3_classes
   - new_S3_class
   - S4_register
-  - S7_class
-  - base_classes
-  - class_missing
 
 articles:
 - title: Learn S7
diff --git a/man/as_class.Rd b/man/as_class.Rd
index 0d8d6f1a..9864f4a3 100644
--- a/man/as_class.Rd
+++ b/man/as_class.Rd
@@ -32,3 +32,4 @@ formal S4 classes.
 as_class(class_logical)
 as_class(new_S3_class("factor"))
 }
+\keyword{internal}
diff --git a/man/base_classes.Rd b/man/base_classes.Rd
index 8c7da50c..6411af27 100644
--- a/man/base_classes.Rd
+++ b/man/base_classes.Rd
@@ -1,5 +1,5 @@
 % Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/base.R, R/S3.R
+% Please edit documentation in R/base.R
 \docType{data}
 \name{base_classes}
 \alias{base_classes}
@@ -16,11 +16,7 @@
 \alias{class_numeric}
 \alias{class_atomic}
 \alias{class_vector}
-\alias{class_factor}
-\alias{class_Date}
-\alias{class_POSIXct}
-\alias{class_data.frame}
-\title{Base classes}
+\title{S7 wrappers for base types}
 \usage{
 class_logical
 
@@ -47,23 +43,13 @@ class_numeric
 class_atomic
 
 class_vector
-
-class_factor
-
-class_Date
-
-class_POSIXct
-
-class_data.frame
 }
 \value{
 S7 classes wrapping around common base types and S3 classes.
 }
 \description{
-These classes represent base types allowing them to be used within S7.
-There are three categories: base types, unions types, and key S3 classes.
-
-Base types:
+The following S7 classes represent base types allowing them to be used
+within S7:
 \itemize{
 \item \code{class_logical}
 \item \code{class_integer}
@@ -77,7 +63,8 @@ Base types:
 \item \code{class_environment} (can only be used for properties)
 }
 
-Union types:
+We also include three union types to model numerics, atomics, and vectors
+respectively:
 \itemize{
 \item \code{class_numeric} is a union of \code{class_integer} and \code{class_double}.
 \item \code{class_atomic} is a union of \code{class_logical}, \code{class_numeric},
@@ -85,14 +72,6 @@ Union types:
 \item \code{class_vector} is a union of \code{class_atomic}, \code{class_list}, and
 \code{class_expression}.
 }
-
-Key S3 classes:
-\itemize{
-\item \code{class_data.frame}
-\item \code{class_Date}
-\item \code{class_factor}
-\item \code{class_POSIXct}
-}
 }
 \examples{
 
diff --git a/man/base_s3_classes.Rd b/man/base_s3_classes.Rd
new file mode 100644
index 00000000..efd2ab93
--- /dev/null
+++ b/man/base_s3_classes.Rd
@@ -0,0 +1,30 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/S3.R
+\docType{data}
+\name{base_s3_classes}
+\alias{base_s3_classes}
+\alias{class_factor}
+\alias{class_Date}
+\alias{class_POSIXct}
+\alias{class_data.frame}
+\title{S7 wrappers for key S3 classes}
+\usage{
+class_factor
+
+class_Date
+
+class_POSIXct
+
+class_data.frame
+}
+\description{
+S7 bundles \link[=new_S3_class]{S3 definitions} for key S3 classes provided by
+the base package:
+\itemize{
+\item \code{class_data.frame} for data frames.
+\item \code{class_Date} for dates.
+\item \code{class_factor} for factors.
+\item \code{class_POSIXct} for \code{POSIXct} date-times.
+}
+}
+\keyword{datasets}
diff --git a/man/class_any.Rd b/man/class_any.Rd
new file mode 100644
index 00000000..7c9afad1
--- /dev/null
+++ b/man/class_any.Rd
@@ -0,0 +1,22 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/special.R
+\docType{data}
+\name{class_any}
+\alias{class_any}
+\title{Dispatch on any class}
+\usage{
+class_any
+}
+\description{
+Use \code{class_any} to register a default method that is called when no other
+methods are matched.
+}
+\examples{
+foo <- new_generic("foo", "x")
+method(foo, class_numeric) <- function(x) "number"
+method(foo, class_any) <- function(x) "fallback"
+
+foo(1)
+foo("x")
+}
+\keyword{datasets}
diff --git a/man/class_missing.Rd b/man/class_missing.Rd
index e0f40e4e..058aa187 100644
--- a/man/class_missing.Rd
+++ b/man/class_missing.Rd
@@ -3,36 +3,24 @@
 \docType{data}
 \name{class_missing}
 \alias{class_missing}
-\alias{class_any}
-\title{Special dispatch types}
-\format{
-An object of class \code{S7_missing} of length 0.
-
-An object of class \code{S7_any} of length 0.
-}
+\title{Dispatch on a missing argument}
 \usage{
 class_missing
-
-class_any
 }
 \value{
 Sentinel objects used for special types of dispatch.
 }
 \description{
-\itemize{
-\item Use \code{class_missing} when the user has not supplied an argument
-\item Use \code{class_any} for a default method that is called only if no other
-methods are matched
-}
+Use \code{class_missing} to dispatch when the user has not supplied an argument,
+i.e. it's missing in the sense of \code{\link[=missing]{missing()}}, not in the sense of
+\code{\link[=is.na]{is.na()}}.
 }
 \examples{
 foo <- new_generic("foo", "x")
-method(foo, class_integer) <- function(x) "integer"
-method(foo, class_missing) <- function(x) "missing"
+method(foo, class_numeric) <- function(x) "number"
 method(foo, class_any) <- function(x) "fallback"
 
 foo(1)
 foo()
-foo("x")
 }
 \keyword{datasets}
diff --git a/man/method-set.Rd b/man/method-set.Rd
index aadf6ec4..102855db 100644
--- a/man/method-set.Rd
+++ b/man/method-set.Rd
@@ -2,7 +2,7 @@
 % Please edit documentation in R/method-register.R
 \name{method<-}
 \alias{method<-}
-\title{Register a S7 method for a generic}
+\title{Register an S7 method for a generic}
 \usage{
 method(generic, signature) <- value
 }
diff --git a/man/method.Rd b/man/method.Rd
index a767d4a9..02fce239 100644
--- a/man/method.Rd
+++ b/man/method.Rd
@@ -2,7 +2,7 @@
 % Please edit documentation in R/method-introspect.R
 \name{method}
 \alias{method}
-\title{Retrieve a method for an S7 generic}
+\title{Find a method for an S7 generic}
 \usage{
 method(generic, class = NULL, object = NULL)
 }
@@ -17,14 +17,15 @@ multiple dispatch then both \code{object} and \code{class} must be a list of
 classes/objects.}
 }
 \value{
-A function with class <S7_method>.
+Either a function with class \code{S7_method} or an error if no
+matching method is found.
 }
 \description{
-\code{method()} takes a generic and signature and retrieves the corresponding
-method. This is rarely needed because most of the time you'll rely on the
-the generic, via \code{\link[=S7_dispatch]{S7_dispatch()}}, to find and call the method for you.
-However, this introspection is useful if you want to see the implementation
-of a specific method.
+\code{method()} takes a generic and class signature and performs method dispatch
+to find the corresponding method implementation. This is rarely needed
+because you'll usually rely on the the generic to do dispatch for you (via
+\code{\link[=S7_dispatch]{S7_dispatch()}}). However, this introspection is useful if you want to see
+the implementation of a specific method.
 }
 \examples{
 # Create a generic and register some methods
diff --git a/man/new_S3_class.Rd b/man/new_S3_class.Rd
index 6e059543..47f5cd66 100644
--- a/man/new_S3_class.Rd
+++ b/man/new_S3_class.Rd
@@ -35,6 +35,7 @@ An S7 definition of an S3 class, i.e. a list with class
 \description{
 To use an S3 class with S7, you must explicitly declare it using
 \code{new_S3_class()} because S3 lacks a formal class definition.
+(Unless it's an important base class already defined in \link{base_s3_classes}.)
 }
 \section{Method dispatch, properties, and unions}{
 There are three ways of using S3 with S7 that only require the S3 class
diff --git a/vignettes/compatibility.Rmd b/vignettes/compatibility.Rmd
index ad370d73..f5382cca 100644
--- a/vignettes/compatibility.Rmd
+++ b/vignettes/compatibility.Rmd
@@ -1,8 +1,8 @@
 ---
-title: "Compatibility"
+title: "Compatibility with S3 and S4"
 output: rmarkdown::html_vignette
 vignette: >
-  %\VignetteIndexEntry{Compatibility}
+  %\VignetteIndexEntry{Compatibility with S3 and S4}
   %\VignetteEngine{knitr::rmarkdown}
   %\VignetteEncoding{UTF-8}
 ---