If we understand the nature of time as the fourth dimension, as Einstein postulated, then time travel is quite possible. It would be no different than traveling in any of the other three spacial directions. Einstein showed us that time is not "absolute" but dependent on our frame of reference. Like the other three dimensions it can become stretched, bent, or compressed. Acceleration, gravity, and speed can all effect how objects move through time.
It can be said that our "natural" progression through time is forward. The present becomes the past and the future becomes the present. Our natural progression through space is along the orbital path of the earth. Yet we can change that with our technology. We can easily blast off in a rocket and move in the opposite direction of earth's orbit, slowing our movement through space. If our space ship is fast enough it could even overcome the momentum of our current direction of travel, moving us back through earth's orbital path.
In the future our technology my allow us to "blast off" and move through time in the opposite direction from our natural progression. Moving back through time instead of forward. We could then pilot our time ship into the past or turn and move into the distant future just as we now fly in whatever direction we chose in our space ships.
At one time people argued that man could never fly, but the Wright Brothers proved differently. Since then man has been to the moon and our probes have gone deep into space. Time travel is possible under our current understanding of space-time. Our technology could very well allow us, at some point, to move through time as we do now through space. What the effects of time travel will be, both on ourselves and our civilization, can only be guessed.