The notion of global hyperbolicity was introduced by Jean Leray in 1952 to obtain global uniqueness of solutions to nonlinear wave equations. Globally hyperbolic spacetimes subsequently turned out to be the right geometric setting not only for the well-posedness of the initial value formulation for the Einstein equations in General Relativity but also for the singularity theorems of Penrose and Hawking and several splitting results in Lorentzian geometry. We review the rich history and omnipresence of global hyperbolicity in General Relativity. Then we present a surprising new characterization of globally hyperbolic spacetimes that makes use of ideas and tools from metric geometry.