  Geroch's theorem about the splitting of globally hyperbolic spacetimes is a
central result in global Lorentzian Geometry. Nevertheless, this result was
obtained at a topological level, and the possibility to obtain a metric (or, at
least, smooth) version has been controversial since its publication in 1970. In
fact, this problem has remained open until a definitive proof, recently
provided by the authors. Our purpose is to summarize the history of the
problem, explain the smooth and metric splitting results (including
smoothability of time functions in stably causal spacetimes), and sketch the
ideas of the solution.
