Advances in technology enable us to record neural responses to many thousands of stimuli from a huge number of channels (e.g., fMRI in humans, two-photon imaging in mice, neuropixel probes in monkeys). Given the unprecedented scale of these data -- collected with incredible effort at enormous expense -- what computational tools can we use to study neural representations in high dimensions? What theoretical insights can we gain about the nature of neural representations from large-scale datasets?