The stimulus space model for neural population activity describes the activity of individual neurons as points localized in a metric stimulus space, with firing rate falling off with distance to individual stimuli. Examples include simple cells in visual cortex, place cells in hippocampus, and grid cells in entorhinal cortex. We will briefly review this model and explain why and how methods from topological data analysis allow us to extract the qualitative structure of such spaces directly from measures of neural population activity. We will discuss challenges that arise when studying whether multiple neural populations encode the same topological structure, and sketch an approach to solving this problem. Finally, we will describe recent computational investigations into learning circular coordinate systems in feed-forward networks that leverage these tools. Time permitting, we will also survey some prior work using topology to study mesoscale structure in white matter tracts in the human brain. No prior knowledge of topological methods will be assumed.