Talk about time travel is puzzling even if it isn't obviously contradictory. Philosophers however are divided about whether time travel involves empirical paradox or some deeper metaphysical incoherence. It is suggested that time travel requires a Parmenidean four-dimensionalist metaphysical conception of the world in time. The possibility of time travel is addressed (mainly) from within a Parmenidean metaphysical framework, which is accepted by David Lewis in his defence of the coherence of time travel. It is argued that time travel raises formidable difficulties which are not satisfactorily resolved by Lewis's ingenious defence of time travel. Objections to time travel considered include: (1) travel to other times is impossible because there is nowhere (or “nowhen”) to go to; (2) the problem that upon setting out on a journey to the past a time machine will collide with itself; (3) time travel generates a mysterious temporal dualism between experiential time and physical time; (4) travel to the past permits reverse causation, raising the possibility of causal loops and attendant problems arising, for example, from the prospect of empirical contradiction and the possibility of someone being one of their ancestors.