We will describe some recent applications of resolution of singularities methods to questions of interest in analysis. In particular, we will describe a recent local resolution of singularities algorithm of the speaker for real-analytic functions. This algorithm is elementary and self-contained, and makes extensive use of Newton polyhedra and local coordinate systems. Some applications will be given. These include applications to oscillatory integrals, asymptotic expansions for sublevel set volumes, and the determination of the supremum of the positive e for which |f|^{- e} is locally integrable. Here f denotes a real-analytic function.