Geometric applications of geometric flows

Over the past 20-30 years, geometric flows have been at the core of spectacular breakthroughs on a wide range of problems in geometry, such as the proof of the Riemannian Penrose conjecture using inverse mean curvature flow, the proof of the geometrisation conjecture using Ricci flow, and the proof that manifolds with 1/4-pinched curvature are space forms using Ricci flow and isotropic curvature.