Is it physically possible for us to time-travel?

I've heard theories that describe time as light passing, so if we travel past the speed of light, we can arrive in the future, but only go back in time to observe what has already happened. In another theory, I read time is non-linear, another dimension, so it is possible for us to manipulate time. What do we know about time-travel so far, and is it feasible for us to travel in the past or future with the physics we know now?