Travelling through time is something we all appear to do every day, this morning I was in the past but now I'm in the present which was the future! I assume however it is about when an individual travels to a time outside of the ordinary scope. There's an interesting article in Le Poidevin & McBeath's book The Philosophy of Time on the subject but I can't remember who wrote it, however here are two key issues.

First if we were to travel back in time it would appear possible that we could change the past, possibly causing a causal loop whereby our actions in the past affect the way we are in the future. Second there is the ontological status of the past and the future.

To deal with the first problem, consider the 'Back to the Future' scenario where the character potentially stops his mum meeting his father and therefore prevents his own existence. If this were to happen however it would not be the case that in the future that he could go back and prevent his own existence. The argument therefore entails that if he can prevent his own existence then he can't prevent his existence. The other apparent way to avoid this problem is to suggest that you can't affect the past when you go back, but this is somewhat strange. The way around this problem is to say that the Time traveller can affect the past however he can't change it. the 'past'' is already a determined system which the time traveller may cause an event in but any event that he causes will have already happened. He is therefore free to affect the past but he cannot change anything that happened in it.

The second issue is whether there is anywhere to travel to. There are two main positions on time which broadly are the tensed view and the tenseless view. Without going into the positions too much the tenseless view of time is that there is nothing ontologically privileged about the 'present' that we perceive, all times are equally real, thus this position is somewhat analogous to the conception most of hold on space where there is nothing special about 'here' rather it is just the place we happen to occupy. If you are a tenseless (b-theorist) theorist then there clearly is a 'place' to go to when you time travel.

The second position that is held is the tensed theory (a-theory) of time whereby there is something privileged about the present, namely it is the only time that is present. Time flows from the future into the present, and the present to the past. One of the main motivations for this position is that it allows us to hold that the future is open and allows for a non-deterministic position of the world. The a-theorist has more work to do than the b-theorist at this point as for the a-theorist three main positions are viable:

a. Only the present exists.
b. The past and the present exist.
c. The past present and future exist.

Now depending on which of a—c you accept you're potential to travel to those places is affected, clearly if you hold a then time travel is a priori impossible, if b then you can't go to the future.

There are other issues but I feel these are the main two. As I say if you have an interest in time I strongly recommend Le Poidevin and McBeath's anthology [The Philosophy of Time. Oxford University Press 1993].