The question whether the universe is a black hole has been raised by various researchers, motivated in part by the fact that the Schwarzschild radius associated with the matter content of the universe is roughly equal to the radius of the observable universe. In this talk, I will review the arguments for and against the claim that the universe is a black hole. I will also discuss the arguments for the claim that black holes can spawn baby universes. The talk is based on a chapter for an upcoming popular science book about black holes.