Deep Learning is a powerful collection of techniques for statistical learning, which has shown dramatic applications in many different directions, including including the study of data sets of images, text, and time series. It uses neural networks, specifically convolutional neural networks (CNN's), to produce these results. What we have observed recently is that methods of topology can contribute to this effort, in diagnosing behavior within the CNN's, in the design of neural networks with excellent computational properties, and in improving generalization, i.e. the transfer of results of one neural network from one data set to another of similar type. We'll discuss topological methods in data science, as well as there application to this interesting set of techniques.