What are we doing when we explain a mental process by saying that the brain performs a computation? What does it mean in general for a physical system to perform a computation? Under what conditions do two physical systems perform the same computation? Is computation a real (objective) property of a physical system, or is it only a property that we project onto the system? In this talk, I explore answers to these questions, a challenge from Putnam that they face, and consequences for computational accounts of the mind.