Time Travel

First of all is it possible? And how?
I'm not going to argue facts about how we might go about ripping the time space continuum and travel through time and space, but I will ask some clearly unanswerable but curious questions.
I was watching the Twilight Zone (the originals, there the best!) and there was an episode on time travel where the men were debating what would happen if you traveled back in time and it lead me to think about a few possibilities.

You might think that when you time travel your presence in the past and anything you do can drastically change the future or your present like in The Butterfly Effect. The other way you may think time travel works is that everything that you do or did was supposed to happen like in the Twilight Zone Episode 'Back Then'. The man mysteriously goes to the past o the night of Lincoln's assassination at Ford Theatre and tries to stop the assassin, but when he goes back to the present he realizes after everything he did the present did not change and in fact because of what he did things are the way they are.

There are so many questions that beget questions on this. I’m not exactly sure what I think, but no matter what you do life will be life and we all go through good and bad, it’s all a circle so whether you changed things or nothing at all thing will turn out the same because everything "changes" so much it actually becomes the same and it's all one.