According to Simulation Theory, to understand what is going on in another person's mind, the observer uses his or her own mind as a model of the other mind. Recently, philosophers and cognitive neuroscientists have proposed that mirror neurones (which fire in response to both executing and observing a goal directed action) provide a plausible neural substrate for simulation, a mechanism for directly perceiving, or 'resonating' with, the contents of other minds. This article makes the case against Simulation Theory, using evidence from cognitive neuroscience, developmental psychology, and social psychology. In particular, the errors that adults and children make when reasoning about other minds are not consistent with the 'resonance' versions of Simulation Theory.