The Ricci flow, a geometric flow equation, was introduced in 1982 as part of a program to resolve Thurston's geometrization conjecture. Interestingly, this flow equation made its appearance even earlier, in physics literature, in 1979. It is the renormalization group flow for the metric in string theory (in a certain approximation). In this talk, I will describe how recent developments in the mathematics of Ricci flow have led to and could be used further to get exciting results in string theory.