In many functionally distinct regions of the brain, populations of neurons form maps of
spaces that the brain seeks to represent. In the early visual system, there is evidence that
the brain organizes such population representations efficiently, minimizing the neural
resources required to reach the fidelity necessary in representing natural stimuli, given an
animal's behavioral needs. I will review this evidence, and will then describe ongoing work
applying this principle of efficiency to the "sense of place" -- i.e. the representation of an
animal's physical location in the "place cell" and "grid cell" systems, which have been
discovered in two parts of the brain, the hippocampus and the entorhinal cortex. If time
permits, I will conclude by briefly discussing how similar analyses can shed light on the
representation of shape in higher visual areas, and on the representation of odors in the
olfactory system.