Systems neuroscience has traditionally progressed by recording neural activity and correlating it with external stimuli or behavior. While this approach has led to many key discoveries, it inherently requires a priori assumptions about the identity of the encoded variables. Recent advances in large-scale neuronal recordings in behaving animals offer an alternative strategy. These high-dimensional datasets, combined with novel analytical tools, enable the application of concepts and methods from  topology to explore neural coding without prior assumptions. Here, I focus on neural systems underlying spatial cognition and present examples where topological approaches offer insight:

1. when the encoded variable is unknown,
2. when the encoded variable is known but the coding scheme is unknown, and
3. when both the encoded variable and coding scheme are well-defined. These cases illustrate how topological frameworks can uncover the variables represented by neural circuits and shed light on the computational processes they support.