Here's a summary of the libraries Embedly provides for developers who want to access Embedly's API programatically.

Official

Libraries developed and maintained by Embedly:

Unofficial

Libraries developed and maintained by the community:

Perl by Greg Heo
.NET by Simon Green
OverblogEmbedlyBundle (Symfony Bundle) by Laurent
Sarrazin
Twig-PHP (Twig PHP lib) by Emanuel
Minotto
embedly-laravel (Laravel 5 package) by Ahmad Elbadawy

Tools

Here is a list of the current tools that easily integrate with Embedly:

Embedly Wordpress

The Embedly WordPress plugin allows bloggers to embed videos, images, and rich media from 325+ sources with just the url. It uses the Embedly API to get the embed code and display it in a post. This plugin extends the Embedly framework in WordPress 3.8 and higher.

Drupal oEmbed

This module will allow your Drupal site to embed content from oEmbed-providers, as well as for the site to become an oEmbed-provider itself, so that other oEmbed-enabled websites can easily embed your content. Since version 6.x-0.6 this module comes with an autoupdating support for embedding content with Embedly.