Theoretically lots of things are possible and time travel is one of those. For my part, I only know about the theory behind travelling forward in time, which, by the way, a misleading statement.
The theory of time travel is actually based on the great physicist and nobelist Albert Einstein’s theory of relativity – theory which may be hard to understand for those lacking the necessary background in physics/mathematics, which is why I will not even consider explaining it. Suffice to say that according to this theory the rate at which time goes on is different in a frame moving fast and one moving slowly, where the frame being considered could be a vehicle – here called a time machine.
According to the theory of relativity, the rate at which time passes is smaller in a frame moving fast, that is, time does go slower when you are moving fast. Now, to get significant enough reductions in the value of the rate of time, the said frame – vehicle – would have to be moving really fast. In theory speeds tending to the value of that of light (300000 km/s) would give very significant reductions in the rate at which time would pass in the vehicle.
This may all seem a little blurry as to how one would actually be travelling in time, but that notion comes forth in the following example:
Consider a vehicle moving at a velocity near that of light; time inside the said vehicle would be passing slowly, compared with time passing on say, planet earth, meaning that one day in the vehicle could mean a month on earth. In fact, at speeds near that of light, a few days in the vehicle could mean hundreds of years on earth.
[Note that the vehicle would not necessary have to be travelling that fast as this can be compensated by more time travelling in the vehicle at a relatively slow speed (of the order of thousands of kilometres per second for significant travel in time)]
Now, the reason why it has not been done , yet, is because of the required speeds to be reached to get fast, significant, time travel. For one, the shearing forces acting on the vehicle would be enormous and materials or designs which could resist such forces have not been found or created yet. In the event we do succeed in creating an appropriate vehicle, there would still be the problem of powering it. In third position, if we want to travel in time, we would have to develop inertial dampeners good enough to prevent our bodies from being crushed into their seats. Though not being able to develop those would not be a problem as I believe that we would be able to programme such a machine to operate itself and indirectly travel in time.
This theory is just ink on paper, just like a good science-fiction story written to amaze people one could say, except that it has been noted that the on board clock of the commercial supersonic aircraft Concorde was indeed late after each voyage by small fractions of time – milliseconds to be precise – which is, to me, a concrete enough proof of the said theory.