diff --git a/docs/reference/gobject/signals.md b/docs/reference/gobject/signals.md
index 0486cd930..ab7444bfd 100644
--- a/docs/reference/gobject/signals.md
+++ b/docs/reference/gobject/signals.md
@@ -14,11 +14,13 @@ through strings. Signals introduced for a parent type are available
 in derived types as well, so basically they are a per-type facility
 that is inherited.
 
+## Handlers
+
 A signal emission mainly involves invocation of a certain set of
 callbacks in precisely defined manner. There are two main categories
 of such callbacks, per-object ones and user provided ones.
-(Although signals can deal with any kind of instantiatable type, I'm
-referring to those types as "object types" in the following, simply
+(Although signals can deal with any kind of instantiatable type, those types are
+referred to as ‘object types’ in the following, simply
 because that is the context most users will encounter signals in.)
 The per-object callbacks are most often referred to as "object method
 handler" or "default (signal) handler", while user provided callbacks are
@@ -29,16 +31,33 @@ frequently happens at the end of an object class' creation), while user
 provided handlers are frequently connected and disconnected to/from a
 certain signal on certain object instances.
 
+A handler must match the type defined by the signal in both its arguments and
+return value (which is often `void`). All handlers take a pointer to the type
+instance as their first argument, and a `gpointer user_data` as their final
+argument, with signal-defined arguments in-between. The `user_data` is always
+filled with the user data provided when the handler was connected to the signal.
+Handlers are documented as having type [type@GObject.Callback], but this is
+simply a generic placeholder type — an artifact of the GSignal APIs being
+polymorphic.
+
+When a signal handler is connected, its first (‘instance’) and final (‘user
+data’) arguments may be swapped if [func@GObject.signal_connect_swapped] is used
+rather than [func@GObject.signal_connect]. This can sometimes be convenient for
+avoiding defining wrapper functions as signal handlers, instead just directly
+passing a function which takes the user data as its first argument.
+
+## Emissions
+
 A signal emission consists of five stages, unless prematurely stopped:
 
 1. Invocation of the object method handler for `G_SIGNAL_RUN_FIRST` signals
 
-2. Invocation of normal user-provided signal handlers (where the @after
+2. Invocation of normal user-provided signal handlers (where the `after`
    flag is not set)
 
 3. Invocation of the object method handler for `G_SIGNAL_RUN_LAST` signals
 
-4. Invocation of user provided signal handlers (where the @after flag is set)
+4. Invocation of user provided signal handlers (where the `after` flag is set)
 
 5. Invocation of the object method handler for `G_SIGNAL_RUN_CLEANUP` signals
 
@@ -64,7 +83,7 @@ detail part of the signal specification upon connection) serves as a
 wildcard and matches any detail argument passed in to emission.
 
 While the `detail` argument is typically used to pass an object property name
-(as with `GObject::notify`), no specific format is mandated for the detail
+(as with [signal@GObject.Object::notify]), no specific format is mandated for the detail
 string, other than that it must be non-empty.
 
 ## Memory management of signal handlers
diff --git a/gobject/gsignal.c b/gobject/gsignal.c
index 755a515d8..a5b471cb3 100644
--- a/gobject/gsignal.c
+++ b/gobject/gsignal.c
@@ -2301,7 +2301,10 @@ g_signal_get_invocation_hint (gpointer instance)
  * If @closure is a floating reference (see g_closure_sink()), this function
  * takes ownership of @closure.
  *
- * Returns: the handler ID (always greater than 0 for successful connections)
+ * This function cannot fail. If the given signal doesn’t exist, a critical
+ * warning is emitted.
+ *
+ * Returns: the handler ID (always greater than 0)
  */
 gulong
 g_signal_connect_closure_by_id (gpointer  instance,
@@ -2366,7 +2369,10 @@ g_signal_connect_closure_by_id (gpointer  instance,
  * If @closure is a floating reference (see g_closure_sink()), this function
  * takes ownership of @closure.
  *
- * Returns: the handler ID (always greater than 0 for successful connections)
+ * This function cannot fail. If the given signal doesn’t exist, a critical
+ * warning is emitted.
+ *
+ * Returns: the handler ID (always greater than 0)
  */
 gulong
 g_signal_connect_closure (gpointer     instance,
@@ -2462,7 +2468,10 @@ node_check_deprecated (const SignalNode *node)
  * used. Specify @connect_flags if you need `..._after()` or
  * `..._swapped()` variants of this function.
  *
- * Returns: the handler ID (always greater than 0 for successful connections)
+ * This function cannot fail. If the given signal doesn’t exist, a critical
+ * warning is emitted.
+ *
+ * Returns: the handler ID (always greater than 0)
  */
 gulong
 g_signal_connect_data (gpointer       instance,
diff --git a/gobject/gsignal.h b/gobject/gsignal.h
index 5522b72bd..52d08a809 100644
--- a/gobject/gsignal.h
+++ b/gobject/gsignal.h
@@ -500,14 +500,18 @@ void   g_signal_chain_from_overridden_handler (gpointer           instance,
  * @c_handler: the #GCallback to connect.
  * @data: data to pass to @c_handler calls.
  * 
- * Connects a #GCallback function to a signal for a particular object.
+ * Connects a [type@GObject.Callback] function to a signal for a particular object.
  * 
- * The handler will be called synchronously, before the default handler of the signal. g_signal_emit() will not return control until all handlers are called.
+ * The handler will be called synchronously, before the default handler of the signal.
+ * [func@GObject.signal_emit] will not return control until all handlers are called.
  *
- * See [memory management of signal handlers][signals.html#Memory_management_of_signal_handlers] for
+ * See [memory management of signal handlers](signals.html#Memory_management_of_signal_handlers) for
  * details on how to handle the return value and memory management of @data.
  * 
- * Returns: the handler ID, of type #gulong (always greater than 0 for successful connections)
+ * This function cannot fail. If the given signal doesn’t exist, a critical
+ * warning is emitted.
+ *
+ * Returns: the handler ID, of type `gulong` (always greater than 0)
  */
 /* Intentionally not using G_CONNECT_DEFAULT here to avoid deprecation
  * warnings with older GLIB_VERSION_MAX_ALLOWED */
@@ -524,7 +528,10 @@ void   g_signal_chain_from_overridden_handler (gpointer           instance,
  * 
  * The handler will be called synchronously, after the default handler of the signal.
  * 
- * Returns: the handler ID, of type #gulong (always greater than 0 for successful connections)
+ * This function cannot fail. If the given signal doesn’t exist, a critical
+ * warning is emitted.
+ *
+ * Returns: the handler ID, of type `gulong` (always greater than 0)
  */
 #define g_signal_connect_after(instance, detailed_signal, c_handler, data) \
     g_signal_connect_data ((instance), (detailed_signal), (c_handler), (data), NULL, G_CONNECT_AFTER)
@@ -562,7 +569,10 @@ void   g_signal_chain_from_overridden_handler (gpointer           instance,
  *                   (GCallback) button_clicked_cb, other_widget);
  * ]|
  * 
- * Returns: the handler ID, of type #gulong (always greater than 0 for successful connections)
+ * This function cannot fail. If the given signal doesn’t exist, a critical
+ * warning is emitted.
+ *
+ * Returns: the handler ID, of type `gulong` (always greater than 0)
  */
 #define g_signal_connect_swapped(instance, detailed_signal, c_handler, data) \
     g_signal_connect_data ((instance), (detailed_signal), (c_handler), (data), NULL, G_CONNECT_SWAPPED)