Note: this list is generated by looking for the string for this theme hook, so it may include some references that are not actually using this theme hook.

ajax_prepare_response in core/includes/ajax.inc
Converts the return value of a page callback into an Ajax commands array.
backdrop_common_theme in core/includes/common.inc
Provides theme registration for themes across .inc files.
config_export_single_form_update_type in core/modules/config/config.admin.inc
Handles switching the configuration type selector.
file_ajax_upload in core/modules/file/file.module
Ajax callback: Processes file uploads and deletions.
file_managed_file_browser_open in core/modules/file/file.module
AJAX callback for managed_file elements to open a browser modal dialog.
filter_admin_format_filter_settings_ajax in core/modules/filter/filter.admin.inc
Ajax handler for buttons in filter_admin_format_filter_settings_form().
filter_admin_format_filter_settings_form_ajax in core/modules/filter/filter.admin.inc
Ajax handler: Opens the dialog to configure a text format filter.
filter_admin_format_form in core/modules/filter/filter.admin.inc
Form constructor for the text format add/edit form.
filter_format_editor_dialog_save in core/modules/filter/filter.pages.inc
Form AJAX callback. Sends the save editor AJAX command and closes the dialog.
hook_ajax_render_alter in core/modules/system/system.api.php
Alter the commands that are sent to the user through the Ajax framework.
installer_manager_install_modal_callback in core/modules/installer/installer.manager.inc
AJAX callback to update the add/remove queue on bulk add.
layout_ajax_form_open_dialog in core/modules/layout/layout.admin.inc
AJAX handler that opens a form in a dialog.
layout_ajax_form_save_dialog in core/modules/layout/layout.admin.inc
AJAX handler that saves a form in a dialog and updates the underlying form.
layout_ajax_form_save_title_dialog in core/modules/layout/layout.admin.inc
AJAX handler that updates the title.
layout_block_configure_ajax_update in core/modules/layout/layout.admin.inc
AJAX callback to update the underlying layout form after updating a block.
layout_block_disable_page in core/modules/layout/layout.admin.inc
Menu callback; Set a block as disabled.
layout_entity_admin_form in core/modules/layout/layout.entity.admin.inc
Render the settings form for listing entity layouts.
layout_flexible_template_configure_form in core/modules/layout/layout.flexible.inc
Form to manage adding and removing rows to a flexible template.
layout_flexible_template_edit_row_ajax in core/modules/layout/layout.flexible.inc
AJAX callback on the submit button for editing a layout row.
layout_menu_item_form in core/modules/layout/layout.admin.inc
Form callback; Configure a layout menu item.
layout_preprocess_layout in core/modules/layout/layout.theme.inc
Prepares variables for layout templates.
layout_settings_form in core/modules/layout/layout.admin.inc
Render the settings form for layout.
layout_settings_form_path_ajax in core/modules/layout/layout.admin.inc
AJAX handler for layout_settings_form().
system_preprocess_page_components in core/modules/system/system.theme.inc
Prepares variables for Page Component block templates.
template_preprocess_maintenance_page in core/includes/theme.inc
Prepares variables for maintenance-page templates.
views_ajax_form_wrapper in core/modules/views/includes/ajax.inc
Wrapper around backdrop_build_form to handle some AJAX stuff automatically. This makes some assumptions about the client.
_filter_image_library_ajax in core/modules/filter/filter.pages.inc
Render the image library.