Black holes, conceived as mathematical possibilities centuries ago, are now established as an astrophysical reality: over 100 million black holes reside within our galaxy alone. Consisting of a singularity, where our current theories of physics break down, and surrounded by an event horizon, from within which no signal can ever escape, they are quite unlike anything else in the Universe. Yet despite their mysterious nature, in the past two decades we have made extraordinary observational breakthroughs in understanding black holes. Rob Fender’s research group has been leading on a series of discoveries using a new generation of vast radio telescope arrays. In this lecture, he will present these breakthroughs, and discuss what lies ahead in the coming decades and centuries.