You are the same person as that small child in your parents’ photo album. What makes this so? Some say that it is because you and that child share a soul. Others that it has to do with spatiotemporal continuity, or the continuity of certain biological processes. The English philosopher John Locke rejected all of those answers, and offered a very different account that has proved influential. According to him, personal identity is a matter of psychological relations — and in particular, memory relations — between your present self and your past self. We will consider the problems and prospects for all of these accounts of personal identity, drawing on the assistance of thought experiments about Star Trek transporters and various sorts of brain transplant operations.