If time travel existed...

How do you think it would work? From what I noticed, most movies and shows have one of these two approaches to time travel; Being able to change the present. Like in Looper, where if you went back and changed something, it would effect the current present. This concept kind of confuses me, I mean, it should make more sense because if you went back and done something differently, naturally you would expect your presented to be affected depending on your actions. However in Looper, they used time travel to send your older self back to be killed by your younger self, so when you done that, then got old once again, would your younger selves keep killing your older selves? Will there be never ending yous and keep living different lives each time? Then there's the whatever you done while time traveling, had already happened, and you cannot change the present no matter what, approach. I think I like this one more, because while you're experiencing it for the first time, you weren't aware that you actually played a part in what happened in the past. Seems more interesting to me and less confusing, because it doesn't matter what you attempt to do while time traveling, whatever had happened, is inevitable. So, if time travel were to exist or if it were to be invented, how do you think it will work? Like one of the two examples I listed, or something different altogether?