This paper presents a critical examination of claims advanced by several philosophers to the effect that 'time travel' represents a physical possibility and that the interpretation of certain actually observed phenomena in terms of 'time travel' is both legitimate and advantageous. It is argued that (a) no convincing motivation for the introduction of the time travel hypothesis has been presented; (b) no coherent and interesting sense of 'going backward in time' has been supplied which makes 'time travel' compatible with Special (...) Relativity; (c) even the conceptual possibility of 'time travel' is an unsettled and somewhat nebulous question. (shrink)