In 2002 a company called Digium was incorporated. It made PBX software based on the open source PBX software called Asterisk which the company founder, Mark Spencer created.
In late 2007, Digium bought a small company called Switchvox which had taken the Asterisk software, simplified PBX management and user operations so that non-tech companies could operate it, and wrapped it up as a turn-key PBX system (This is a great simplification, but you get the idea).
Recently Switchvox announced the Switchvox Extend API and Switchvox Developer Central which is a portal for Switchvox integration developers. One of the coolest features of this site is the API Test Suite which allows you to make any Extend API call to your Switchvox system. It displays both the request and response data.
If you want to check-out the Switchvox Extend API but don't own a Switchvox PBX, you can get a free account on the demo server and use the Test Suite with that.
Just one disclaimer - I'm a former employee of Switchvox.