Ricci flow is a generalization of the heat equation for Riemannian
metrics. It plays a role in quantum field theory and string theory,
and has proven to be a useful tool in the study of three-manifold
topology. I will start with an introduction, from a physicist's
viewpoint, to the flow and its general properties. I will then discuss
novel applications of the flow to the geometry of black holes and to
the numerical solution of the Einstein equation.