Over the past 15 years, our ability to collect massive data sets has increased dramatically. Concomitantly, our need to process, compress, store, analyze, and summarize these data sets has grown as well. Scientific, engineering, medical, and industrial applications require that we carry out these tasks efficiently and reasonably accurately. Data streams are one type of modern massive data sets, characterized by their size and by their distributed and dynamic properties. We give an expository discussion of data stream models and the algorithmic challenges that these models pose for computational statistical analysis, then present an overview of three streaming algorithms and a discussion of the computational challenges with each.