In 1968, Friedhelm Waldhausen posed the following conjecture: every closed, irreducible 3-manifold has a finite-sheeted cover contains an incompressible surface. After more than 40 years with essentially minimal progress, this conjecture fell in Spring 2012, due to the combined efforts of Ian Agol, Jeremy Kahn, Vladimir Markovic, and Daniel Wise, plus significant input from several others.

In addition to proving Waldhausen's conjecture, their solution established several other stunning and unexpected results about 3--manifolds, particularly hyperbolic 3-manifolds. The ingredients of the proof range from ergodic theory to group theory. I will survey some of the context of the conjecture and give a top-level outline of the proof.