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. We will briefly review this model, and discuss how methods from topological data analysis allow us to extract qualitative structure and coordinate systems for such spaces from measures of neural population activity. We will briefly explore challenges that arise when studying whether and how multiple neural populations encode the same topological structure, and discuss recent experiments involving Hebbian learning for circular coordinate systems in feed-forward networks. No prior knowledge of topological methods will be assumed.