I shall try in this paper to give a brief survey of a few recent and very exciting developments in the application of analysis on Lipschitz manifolds to geometric topology. As will eventually become apparent, this work involves both operator algebras (especially the connection between C*-algebras and K-theory) and harmonic analysis (in the literal sense of analysis of harmonics, i.e., of the spectrum of the Laplacian) in the proofs, though not in the statements of most of the theorems. Some of these results could only be obtained with great difficulty (if at all) by more traditional topological methods. I will give references to the literature but no proofs. The parts of this work that are my own are joint work with Shmuel Weinberger .