As opposed to jetlag, road trips, or forms of intuitive regular travel (not the LI expressway) there are two kinds of time travel under consideration. First, from physics is the agreed-upon Relativistic (this is kevin’s terming, not from the literature) travel, as per Ender from Orson Scott Card’s series. Relativistic travel is forward only, and not all that interesting for sci-fi.
As per Nick and Kevin, the discussion of relativistic time travel begins with Einstienian realization that time is relative and with the production of the twin paradox. You know this one: twins are born “simultaneously” on Earth. You put one in a space ship moving at the speed of light to a point one light year away. By the time it returns (two years spaceship time), 200 years have passed on Earth. One twin is 200 – and likely dead – the other is 2. Because of special relativity, time works one way only. It is agreed that if you can build the space ship, this is a legitimate form of time travel.
For the interest of the science fiction, other forms of time travel bring up the problems of causation. Enter the grandfather paradox: Tom cannot go back into the past and kill his grandfather or else his father will not have been born to bear Tom. (Oh. note the use of the past perfect…).
Kevin once mentioned that if time is not a closed loop (i.e., we relax the assumptions on causality), then Tom is perfectly capable of killing his grandfather given that he can travel into the past. Tom can live out his days in his grandfather’s time even though he’ll eventually never be born. I lost my damn notes, but I think that “time travel of the Hawking-Ellis variety” uses this assumption.
There will eventually be a series of topics summarizing what we’ve bothered to figure out about time travel.
Twin Paradox – the speed of light and time travel.
Grandfather paradox and the First Principle Paradox of Time Travel. – causality and time travel
Hawking-Ellis Variety Time Travel

See also:
Orson Scott Card, The Terminator, Time Traxx