Just as the theory of general relativity gave a huge impetus to the study of Riemannian geometry, now string theory is motivating important developments in many subfields of geometry, and suggesting remarkable generalizations of classical notions. We give a broad survey of these developments, beginning with the application of classical and modern results in algebraic geometry to the study of the heterotic string on Calabi-Yau manifolds, and then its generalizations to other string theories, involving manifolds of special holonomy. We then explain the sense in which conformal field theory provides string theoretic generalizations of much of this geometry, and how many of the new stringy phenomena such as T-duality and mirror symmetry can be understood in terms of noncommutative geometry, both operator algebraic (a la Connes) and algebraic geometric (a la Kontsevich). We conclude with a brief introduction to the problem of counting realistic vacua, as a prelude to the Feb 22 colloquium of Steve Zelditch.