1) Traveling forward through time: It has been shown as recently as this year that there are in fact particles that move faster than the speed of light, and travel near the speed of light is a way of "emulating" time travel so to speak. When moving at that speed time would still pass in the same way to you but what for you is only hours, days, or months could be years, decades, or even centuries on the far end of the spectrum for those still in normal space. You would in effect be traveling forward in time from your own perspective
2) Traveling back: There is research pointing to subatomic particles having a "memory" of sorts such that if analyzed in the right way one could understand their orientation and energy state as it existed at any past moment at time. If you had a device capable of doing so and had access to the necessary energy you could recreate any past environment exactly as it was, and with the exception of the randomness of discussed by quantum theory, from that point onward this new timeline would play itself out almost exactly as it did previously. The only way there could be any major deviations is if act by humans cause it, and that could only result if we have free will, which is another argument entirely, albeit a very interesting one.
Time travel seems entirely plausible, the only question is if we will invent or discover the means by which to achieve it.