Gravity in spacetimes with more than 3 spacelike directions admit an exciting variety of black hole solutions. This is very different from 3+1-dimensions, where black holes are limited by uniqueness theorems. Recently a new exact solution to the 4+1D vacuum Einstein's equations has been constructed. It describes "Black Saturn": a ring-shaped black hole balanced by rotation around a spherical black hole. In the talk I will review the currently known black hole solutions, describe a powerful solution finding technique, and discuss the "phase diagram" for 4+1d black holes.