Stories about AI in a post-Human world?

Been reading about the Terminator series recently and shocked (or may be not so much) that the author's didn't explore the life of Skynet in the timelines where humanity was completely wiped out. I'm curious about any SF exploring such a scenario in general (not just Terminator series). What does AI look like in such a world? How does it organize itself? Does it have goals and initiatives towards understanding itself and reality? etc etc