Proxima Centauri), about 4.2 light-years away. That is about 25 trillion miles, and even if Voyager 1, one of the fastest probes even launched, was going in the right direction it would take about 75,000 years.
So if you wanted to go into deep space, see another civilization, and make it back before everything you ever knew was destroyed through death and decay, you will need a fast ride. But even if you had a machine that could go nearly the speed of light, observers on earth would have to wait a lifetime for you to just drop off a pizza and return from Vega, a nearby star. And if you wanted to cross the galaxy and come back, a friend on earth would have to wait over 200,000 years, even if you went light-speed. (Notice how I keep giving the time for the observer on Earth; I'm avoiding all the time dilation issues of special relativity.)
So if we really, really want to go places, we need a way to go faster than light. But Einstein's special relativity says no; anything with mass must go less than light. Wah!
But physicists are clever, and we have used Einstein's own theories to find a way. How?
Well, there is another major theory Einstein worked on, the general theory of relativity. It's taking his special relativity but making it more general. While special relativity (SR) dealt with things moving with constant velocities, general relativity (GR) also dealt with acceleration (changing velocities). Moreover, GR explains gravity. See, that Einstein guy was smart. But how can GR help us get past the problem from SR of going faster than light?
Well, there was an interesting solution to GR done by Miguel Alcubierre from Mexico (he completed his PhD in physics at Cardiff) back in 1994. In GR it is possible to mess with the fabric of space and time (space-time) in a way that stretches out space in front and crunches it up from behind. What this means is that in your own local "bubble" of space-time you travel below light-speed, but the bubble itself is flying forward and can go much faster; this is because it is the space that is in effect moving, not a body. This is shown with the Alcubierre metric.
Now, there are issues with this, one of them being the need for a significant amount of negative mass-energies. While it is possible to have negative mass-energy (such as see in the Casimir effect), it is in very small quantities. But the real problem is the quantity. The energy requirements have been explosively huge if you want a ship of any decent size. One early estimate put the mass-energy needed at 10^64 kilograms (a 1 with 64 zeroes after it), which is more than all the mass-energy in the observable universe (the mass of the Milky Way is around 10^42 kg including the dark matter)! It's not happening. Another estimate was made using different assumptions of the space-time geometry and volume inside to get mass-energies on the order of solar or planetary masses. That is still huge, but not impossible. (When I mean planetary masses, I mean turning the entire mass of the planet into pure energy, a process releasing far more than would nuclear fusion or fission.)
But now it seems a team at NASA has further tried to adjust the geometry of the space-time around such a ship to get much more useful energy scales. How small now? They are talking masses of around 1000 kg (they say around the mass of Voyager 1). For an idea of how much energy that is, I converted it to megatons of TNT and found something around 20,000. A Tsar hydrogen fusion bomb has a warhead with 50 megatons, so we are talking about 400 H-bombs. Another way to put it, this is an energy level close to how much the US consumes in a given year. That is a lot of energy, but manageable given the infrastructure.
100 Year Starship Symposium), but I am guessing this was figured using a computer program that will adjust how space-time is bent by changing the conditions of the ring a bit at a time and finding an optimal energy requirement. When it comes to using GR, in classes you will have to solve things by hand, but in reality computers are usually called on for figuring out solutions, especially when there isn't a simple geometry of matter being used (it's easier to figure out the solution when there is symmetry than otherwise).
This is very exciting! This is putting interstellar travel even closer into the hands of future humans. Heck, if things could be this cheery, I may get to see the first interstellar ships before I die! Come on, this would be the definition of awesome. It's also important because if humans remain on Earth we risk becoming extinct. One major disaster, such as a large asteroid impact, and we're done.
Of course, much testing is needed. Harold "Sonny" White, who made the announcement, is talking of using lasers in the lab to perturb space-time on very small scales to see if he can get the idea to work. But again, on very small scales. Moreover, there are other physical problems with any Alcubierre-based warp drive, including the need for sending out signals. And we still need the significant amounts of negative mass-energy (and of considerable density). This isn't something we are going to do in our garages. And there may still be physical problems in any proposal (this paper for 1999 summarizes that, though in technical language.)
Nonetheless, there has been some amazing advances in this area in less than 20 years of research (much of it probably not at the forefront of theoretical physics works). In another 20, perhaps the concept can be demonstrated at a small but macroscopic level (if other physical problems can be resolved). We live in exciting times!