Creating information and knowledge from large and complex data sets is one the fundamental intellectual challenges currently being faced by the mathematical sciences. One approach to this problem comes from the mathematical subdiscipline called topology, which is the study of shape and of its higher dimensional analogues. This subject has thrived as a field within pure mathematics, but the last fifteen years has seen the development of topological methods for studying data sets, which are modeled as point clouds or finite metric spaces. I will survey this work, with examples.
