Index: src/wp-admin/css/customize-controls.css
===================================================================
--- src/wp-admin/css/customize-controls.css	(revision 28731)
+++ src/wp-admin/css/customize-controls.css	(working copy)
@@ -143,6 +143,52 @@
 	margin: 0;
 }
 
+.control-section .accordion-section-title {
+	padding-left: 45px;
+}
+
+.control-section .accordion-section-title:before {
+	font: normal 20px/1 dashicons;
+	position: absolute;
+	top: 11px;
+	left: 14px;
+	-webkit-font-smoothing: antialiased;
+	-moz-osx-font-smoothing: grayscale;
+}
+
+/* Don't override custom icons, which get an additional class. */
+.control-section [class="accordion-section-title "]:before {
+	content: "\f111";
+}
+
+#accordion-section-title_tagline .accordion-section-title:before {
+	content: "\f175";
+}
+
+#accordion-section-colors .accordion-section-title:before {
+	content: "\f309";
+}
+
+#accordion-section-header_image .accordion-section-title:before {
+	content: "\f129";
+}
+
+#accordion-section-background_image .accordion-section-title:before {
+	content: "\f128";
+}
+
+#accordion-section-nav .accordion-section-title:before {
+	content: "\f333";
+}
+
+#accordion-section-static_front_page .accordion-section-title:before {
+	content: "\f109";
+}
+
+.accordion-section[id^="accordion-section-sidebar-widgets"] .accordion-section-title:before {
+	content: "\f116";
+}
+
 .customize-control {
 	width: 100%;
 	float: left;
Index: src/wp-includes/class-wp-customize-section.php
===================================================================
--- src/wp-includes/class-wp-customize-section.php	(revision 28731)
+++ src/wp-includes/class-wp-customize-section.php	(working copy)
@@ -65,6 +65,15 @@
 	public $title = '';
 
 	/**
+	 * Icon for the section to show in UI.
+	 *
+	 * @since 4.0.0
+	 * @access public
+	 * @var string
+	 */
+	public $icon = '';
+
+	/**
 	 * Description to show in the UI.
 	 *
 	 * @since 3.4.0
@@ -164,7 +173,7 @@
 	protected function render() {
 		?>
 		<li id="accordion-section-<?php echo esc_attr( $this->id ); ?>" class="control-section accordion-section">
-			<h3 class="accordion-section-title" tabindex="0"><?php echo esc_html( $this->title ); ?></h3>
+			<h3 class="accordion-section-title <?php echo esc_attr( $this->icon ); ?>" tabindex="0"><?php echo esc_html( $this->title ); ?></h3>
 			<ul class="accordion-section-content">
 				<?php if ( ! empty( $this->description ) ) : ?>
 				<li><p class="description"><?php echo $this->description; ?></p></li>