In November 1915 Einstein finally arrived at the definitive formulation of General Relativity. Before the end of that same year, Schwarzschild found its most important solution. But none of these two men lived to recognize what this solution actually describes: a black hole --- indeed, Einstein's worst blunder was to blind himself to this possibility. Along these hundred years black holes have gradually risen to prominence within the theory, and are nowadays pointing the way to a new understanding of gravity and spacetime. In this talk, I'll introduce, with historical asides, the unfolding of these developments, finishing with current controversies about the reality of black holes when confronted with quantum mechanics.