In the wake of the release of the full trailer for Christopher Nolan's upcoming movie Interstellar, 'Sploid' has produced a short article summarising the latest theoretical thinking on faster-than-light travel. Read it here (and watch the trailer there too).
The important things to remember are:
a) This is all very theoretical at the moment, and the questions about the energy requirements for warping space-time are still unanswered;
b) If the energy requirements are feasible, there will still be limitations on what we can produce. The "just punch it and you're there" comments in the subscript reveals a complete misunderstanding of the nature of the theoretical requirements. It will take vastly more energy to warp space sufficiently to travel at ten times the speed of light than at light speed itself, and orders of magnitude more to travel at higher speeds still. While interstellar travel through our local neighbourhood might be worth aiming for, travel across the galaxy is another major step beyond that. Intergalactic travel is likely to be simply unfeasible.
c) However, relativistic problems are, indeed, irrelevant. According to all current understanding, baryonic matter and known forms of energy cannot exceed the speed of light. Indeed, nothing with an intrinsic rest mass could even reach it. However, an object within a warp field would not be travelling at superluminal speeds. It would be stationary relative to its own bubble of space, but the bubble itself would be shifting relative to its surroundings. By contracting space-time ahead of a ship and expanding it behind it, apparent superluminal speeds could be achieved without any relativistic effects or breaking the light barrier.
d) Even if the physicists demonstrate that this is possible for low mass experiments, we're a long, long way from developing actual warp drives for spacecraft.
e) The fact that we will very likely run out of drinkable water in the near future due to global temperatures rising and ever-growing populations is more of a major concern. I'm with the author on that, all the way. How flying to other star systems is going to help with that, I don't know. No matter how earthlike a planet is, it isn't going to be anywhere near as suitable for us as even a depleted Earth.
Film looks good though.