Is there an API (officially or unofficially) for Google Voice? I would like to have an API to work with voicemails, send/receive SMS messages, initiate calls, etc.
What is the Android client using? Something internal? Has anyone documented it?
No, there is no API for Google Voice announced as of 2021.
"pygooglevoice" can perform most of the voice functions from Python. It can send SMS. I've developed code to receive SMS messages, but the overhead is excessive given the current Google Voice interface. Each poll returns over 100K of content, so you'd use a quarter-gigabyte a day just polling every 30 seconds. There's a discussion on Google Code about this.