I will start by presenting some Hellinger accuracy results for the Nonparametric Maximum Likelihood Estimator (NPMLE) for Gaussian location mixture densities. I will then present two applications of the NPMLE: (a) empirical Bayes estimation of multivariate normal means, and (b) a multiple hypothesis testing problem involving univariate normal means. I will also talk about an extension to the mixture of linear regressions model. This is based on joint work with several collaborators who will be mentioned during the talk.