I will survey the classification of extremal horizons in vacuum spacetimes (including a cosmological constant) and present a recent rigidity theorem which shows that the intrinsic geometry of compact cross-sections of such horizons must admit a Killing vector field. In particular, this implies that the extremal Kerr horizon is the most general such horizon in four-dimensional General Relativity, completing their classification. I will also discuss the application of such horizon rigidity to the corresponding black hole classification, including a recent uniqueness theorem which shows that the extremal Schwarzschild de Sitter spacetime (or its near-horizon geometry) is the only analytic Einstein spacetime with positive cosmological constant that contains a static extremal horizon with a compact cross-section.