Externally observable components of human actions carry only a tiny fraction of the information that matters. Human observers are vastly more interested in perceiving or inferring the mental states - the beliefs, desires and intentions - that lie behind the observable shell. If a person checks her watch, is she uncertain about the time, late for an appointment, or bored with the conversation? If a person shoots his friend on a hunting trip, did he intend revenge or just mistake his friend for a partridge? The mechanism people use to infer and reason about another person’s states of mind is called a ‘Theory of Mind’ (ToM). One of the most striking discoveries of recent human cognitive neuroscience is that there is a group of brain regions in human cortex that selectively and specifically underlie this mechanism. I will describe recent studies from my lab characterising the functional profile of one of these regions, the right temporo-parietal junction. The challenge for the future remains: to construct an adequate computational description of a neurally implemented mechanism, that could reason about another person's thoughts.