Some example use-cases for the Server Timing API in the Performance Lab plugin (see https://github.com/WordPress/performance/pull/553). This example is outdated (see comment below)!

perflab-server-timing-examples.php

<?php
add_action(
	'perflab_server_timing_init',
	function( $server_timing ) {
		// Utility function that returns a measuring callback for an action hook.
		$measure_action = function( $action ) {
			return function ( $metric ) use ( $action ) {
				$start_time = null;

				// If action is already running, at least measure the remainder.
				if ( doing_action( $action ) ) {
					$start_time = microtime( true );
				} else {
					add_action(
						$action,
						function() use ( &$start_time ) {
							$start_time = microtime( true );
						},
						PHP_INT_MIN
					);
				}
				add_action(
					$action,
					function() use ( &$start_time, $metric ) {
						if ( null === $start_time ) {
							return;
						}
						$metric->set_value( ( microtime( true ) - $start_time ) * 1000.0 );
					},
					PHP_INT_MAX
				);
			};
		};

		// The 'plugins_loaded' action hook.
		$server_timing->register_metric(
			'plugins-loaded',
			array(
				'measure_callback' => $measure_action( 'plugins_loaded' ),
				'access_cap'       => 'exist',
			)
		);

		// The 'after_setup_theme' action hook.
		$server_timing->register_metric(
			'after-setup-theme',
			array(
				'measure_callback' => $measure_action( 'after_setup_theme' ),
				'access_cap'       => 'exist',
			)
		);

		// The 'init' action hook.
		$server_timing->register_metric(
			'init',
			array(
				'measure_callback' => $measure_action( 'init' ),
				'access_cap'       => 'exist',
			)
		);

		// The 'wp_loaded' action hook.
		$server_timing->register_metric(
			'loaded',
			array(
				'measure_callback' => $measure_action( 'wp_loaded' ),
				'access_cap'       => 'exist',
			)
		);

		// Time it takes to parse the request (including, but not exclusively, the 'parse_request' action hook).
		$server_timing->register_metric(
			'parse-request',
			array(
				'measure_callback' => function( $metric ) {
					$start_time = null;

					add_filter(
						'do_parse_request',
						function( $passthrough ) use ( &$start_time ) {
							$start_time = microtime( true );
							return $passthrough;
						},
						PHP_INT_MAX
					);
					add_action(
						'parse_request',
						function() use ( &$start_time, $metric ) {
							if ( null === $start_time ) {
								return;
							}
							$metric->set_value( ( microtime( true ) - $start_time ) * 1000.0 );
						},
						PHP_INT_MAX
					);
				},
				'access_cap'       => 'exist',
			)
		);

		// The 'template_redirect' action hook.
		$server_timing->register_metric(
			'template-redirect',
			array(
				'measure_callback' => $measure_action( 'template_redirect' ),
				'access_cap'       => 'exist',
			)
		);

		// Time it takes to locate the template.
		$server_timing->register_metric(
			'locate-template',
			array(
				'measure_callback' => function( $metric ) {
					$start_time = null;

					add_action(
						'template_redirect',
						function() use ( &$start_time ) {
							$start_time = microtime( true );
						},
						PHP_INT_MAX
					);
					add_filter(
						'template_include',
						function( $passthrough ) use ( &$start_time, $metric ) {
							if ( null === $start_time ) {
								return $passthrough;
							}
							$metric->set_value( ( microtime( true ) - $start_time ) * 1000.0 );
							return $passthrough;
						},
						PHP_INT_MIN
					);
				},
				'access_cap'       => 'exist',
			)
		);

		if ( perflab_server_timing_use_output_buffer() ) {
			// The 'wp_head' action hook.
			$server_timing->register_metric(
				'head',
				array(
					'measure_callback' => $measure_action( 'wp_head' ),
					'access_cap'       => 'exist',
				)
			);

			// The 'wp_footer' action hook.
			$server_timing->register_metric(
				'footer',
				array(
					'measure_callback' => $measure_action( 'wp_footer' ),
					'access_cap'       => 'exist',
				)
			);
		}

		// The query to autoload options.
		$server_timing->register_metric(
			'load-alloptions-query',
			array(
				'measure_callback' => function( $metric ) {
					// The query is already run prior to plugins loading, so clear the cache here unless it is a
					// persistent cache. Obviously that's still not good for performance, therefore this measurement
					// should be limited to administrators.
					if ( ! wp_using_ext_object_cache() ) {
						wp_cache_delete( 'alloptions', 'options' );
					}

					$start_time = null;
					add_filter(
						'query',
						function( $query ) use ( &$start_time ) {
							global $wpdb;
							if ( "SELECT option_name, option_value FROM $wpdb->options WHERE autoload = 'yes'" === $query ) {
								$start_time = microtime( true );
							}
							return $query;
						}
					);
					add_filter(
						'pre_cache_alloptions',
						function( $alloptions ) use ( &$start_time, $metric ) {
							if ( null === $start_time ) {
								return $alloptions;
							}
							$metric->set_value( ( microtime( true ) - $start_time ) * 1000.0 );
							return $alloptions;
						}
					);
				},
				// Limit this measurement to administrators (see above for why).
				'access_cap'       => 'manage_options',
			)
		);
	}
);

This example is outdated and only works against a previous implementation of the API prior to WordPress/performance@51c4222. An updated version of this Gist can be found at https://gist.github.com/felixarntz/43fb19e6491a1bc65a7e930dace17c47.