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There are many theories of time travel, but the one that I think is the most likely is the branching-universe theory. In that theory, every time you travel through time the timeline splits. In one timeline you did travel through time and in the other you did not. Also, when you arrive the timeline splits once again.
The advantage of this theory is that paradoxes (such as the grandfather paradox) are impossible. This is due to the fact that when you travel through time you can never return to your original timeline (where you didn't travel through time), and each trip cuts you off from the previous timeline you were on. Any changes you make won't affect you since your personal timeline (unlike the common timeline) is essentially a thread that starts at the point you first travelled through time and tracks all of your jumps until your current point in time.
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