diff --git a/crates/typst-library/src/foundations/label.rs b/crates/typst-library/src/foundations/label.rs
index 5a9e76538..e326a4fa9 100644
--- a/crates/typst-library/src/foundations/label.rs
+++ b/crates/typst-library/src/foundations/label.rs
@@ -75,7 +75,10 @@ impl Label {
     /// Creates a label from a string.
     #[func(constructor)]
     pub fn construct(
-        /// The name of the label. Must not be empty.
+        /// The name of the label.
+        ///
+        /// Unlike the [dedicated syntax](#syntax), this constructor accepts
+        /// any non-empty string, including names with special characters.
         name: Str,
     ) -> StrResult<Label> {
         if name.is_empty() {
diff --git a/crates/typst-library/src/introspection/counter.rs b/crates/typst-library/src/introspection/counter.rs
index c7d26040c..b3801a049 100644
--- a/crates/typst-library/src/introspection/counter.rs
+++ b/crates/typst-library/src/introspection/counter.rs
@@ -407,7 +407,7 @@ impl Counter {
     /// Create a new counter identified by a key.
     #[func(constructor)]
     pub fn construct(
-        /// The key that identifies this counter.
+        /// The key that identifies this counter globally.
         ///
         /// - If it is a string, creates a custom counter that is only affected
         ///   by manual updates,
diff --git a/crates/typst-library/src/introspection/state.rs b/crates/typst-library/src/introspection/state.rs
index c7d1a5be5..7f2832604 100644
--- a/crates/typst-library/src/introspection/state.rs
+++ b/crates/typst-library/src/introspection/state.rs
@@ -273,8 +273,31 @@ impl State {
     #[func(constructor)]
     pub fn construct(
         /// The key that identifies this state.
+        ///
+        /// Any [updates]($state.update) to the state will be identified with
+        /// the string key. If you construct multiple states with the same
+        /// `key`, then updating any one will affect all of them.
         key: Str,
         /// The initial value of the state.
+        ///
+        /// If you construct multiple states with the same `key` but different
+        /// `init` values, they will each use their own initial value but share
+        /// updates. Specifically, the value of a state at some location in the
+        /// document will be computed from that state's initial value and all
+        /// preceding updates for the state's key.
+        ///
+        /// ```example
+        /// #let banana = state("key", "🍌")
+        /// #let broccoli = state("key", "🥦")
+        ///
+        /// #banana.update(it => it + "😋")
+        ///
+        /// #context [
+        ///   - #state("key", "🍎").get()
+        ///   - #banana.get()
+        ///   - #broccoli.get()
+        /// ]
+        /// ```
         #[default]
         init: Value,
     ) -> State {
@@ -328,7 +351,7 @@ impl State {
         Ok(sequence.last().unwrap().clone())
     }
 
-    /// Update the value of the state.
+    /// Updates the value of the state.
     ///
     /// The update will be in effect at the position where the returned content
     /// is inserted into the document. If you don't put the output into the
@@ -336,13 +359,44 @@ impl State {
     /// write `{let _ = state("key").update(7)}`. State updates are always
     /// applied in layout order and in that case, Typst wouldn't know when to
     /// update the state.
+    ///
+    /// In contrast to [`get`]($state.get), [`at`]($state.at), and
+    /// [`final`]($state.final), this function does not require [context].
     #[func]
     pub fn update(
         self,
         span: Span,
-        /// If given a non function-value, sets the state to that value. If
-        /// given a function, that function receives the previous state and has
-        /// to return the new state.
+        /// A value to update to or a function to update with.
+        ///
+        /// - If given a non-function value, sets the state to that value.
+        /// - If given a function, that function receives the state's previous
+        ///   value and has to return the state's new value.
+        ///
+        /// When updating the state based on its previous value, you should
+        /// prefer the function form instead of retrieving the previous value
+        /// from the [context]($context). This allows the compiler to resolve
+        /// the final state efficiently, minimizing the number of
+        /// [layout iterations]($context/#compiler-iterations) required.
+        ///
+        /// In the following example, `{fill.update(f => not f)}` will paint odd
+        /// [items in the bullet list]($list.item) as expected. However, if it's
+        /// replaced with `{context fill.update(not fill.get())}`, then layout
+        /// will not converge within 5 attempts, as each update will take one
+        /// additional iteration to propagate.
+        ///
+        /// ```example
+        /// #let fill = state("fill", false)
+        ///
+        /// #show list.item: it => {
+        ///   fill.update(f => not f)
+        ///   context {
+        ///     set text(fill: fuchsia) if fill.get()
+        ///     it
+        ///   }
+        /// }
+        ///
+        /// #lorem(5).split().map(list.item).join()
+        /// ```
         update: StateUpdate,
     ) -> Content {
         StateUpdateElem::new(self.key, update).pack().spanned(span)
diff --git a/docs/reference/language/scripting.md b/docs/reference/language/scripting.md
index 5e0f1555e..ec7dc1fd9 100644
--- a/docs/reference/language/scripting.md
+++ b/docs/reference/language/scripting.md
@@ -14,7 +14,7 @@ provides compact syntax to embed a code expression into markup: An expression is
 introduced with a hash (`#`) and normal markup parsing resumes after the
 expression is finished. If a character would continue the expression but should
 be interpreted as text, the expression can forcibly be ended with a semicolon
-(`;`).
+(`;`). You can [escape a literal `#` or `;` with a backslash]($syntax/#escapes).
 
 ```example
 #emph[Hello] \
@@ -66,6 +66,7 @@ Content and code blocks can be nested arbitrarily. In the example below,
 ## Bindings and Destructuring { #bindings }
 As already demonstrated above, variables can be defined with `{let}` bindings.
 The variable is assigned the value of the expression that follows the `=` sign.
+A [valid variable name](#identifiers) may contain `-`, but cannot start with `-`.
 The assignment of a value is optional, if no value is assigned, the variable
 will be initialized as `{none}`. The `{let}` keyword can also be used to create
 a [custom named function]($function/#defining-functions). Variables can be
@@ -77,8 +78,8 @@ is no containing block).
 This is #name's documentation.
 It explains #name.
 
-#let add(x, y) = x + y
-Sum is #add(2, 3).
+#let my-add(x, y) = x + y
+Sum is #my-add(2, 3).
 ```
 
 Let bindings can also be used to destructure [arrays]($array) and
diff --git a/docs/reference/language/syntax.md b/docs/reference/language/syntax.md
index fdc4d154a..9fa240273 100644
--- a/docs/reference/language/syntax.md
+++ b/docs/reference/language/syntax.md
@@ -168,6 +168,34 @@ I got an ice cream for
 \$1.50! \u{1f600}
 ```
 
+## Identifiers
+Names of variables, functions, and so on (_identifiers_) can contain letters,
+numbers, hyphens (`-`), and underscores (`_`). They must start with a letter or
+an underscore.
+
+More specifically, the identifier syntax in Typst is based on the
+[Unicode Standard Annex #31](https://www.unicode.org/reports/tr31/), with two
+extensions: Allowing `_` as a starting character, and allowing both `_` and `-`
+as continuing characters.
+
+For multi-word identifiers, the recommended case convention is
+[Kebab case](https://en.wikipedia.org/wiki/Letter_case#Kebab_case). In Kebab
+case, words are written in lowercase and separated by hyphens (as in
+`top-edge`). This is especially relevant when developing modules and packages
+for others to use, as it keeps things predictable.
+
+```example
+#let kebab-case = [Using hyphen]
+#let _schön = "😊"
+#let 始料不及 = "😱"
+#let π = calc.pi
+
+#kebab-case
+#if -π < 0 { _schön } else { 始料不及 }
+// -π means -1 * π,
+// so it's not a valid identifier
+```
+
 ## Paths
 Typst has various features that require a file path to reference external
 resources such as images, Typst files, or data files. Paths are represented as