One of the slightly more bizarre things that Einstein predicted to go along with all of his relativity and whatnot was a phenomenon called gravitational waves, where waves of gravitational energy would propagate through the fabric of space itself. We've never managed to catch one in action, but astronomers have found new evidence that they exist.
You can think of a gravity wave like ripples on a pond, where the pond is a four-dimensional representation of our entire Universe. Got that? Cool. Making a gravity wave is not as simple as tossing a rock into our Universe-pond (or Pondiverse) from the fifth dimension, however: according to Einstein, you only get gravity waves from massive, moving objects like stars caught up in binary systems.
So we sort of know where to look for gravity waves, but actually detecting them is another matter entirely. To see one, we have to somehow measure a ripple in space, which is (to put it mildly) a little bit tricky. The way to do it seems to be to use lasers to precisely measure the distance between two detectors, and if you see that distance grow and shrink a very tiny amount, it could be due to a gravity wave expanding and contracting the very space between the detectors. We've had this sort of experiment set up and running, but we haven't found anything yet: the most advanced gravity wave detector, LIGO, is a giant laser interferometer that can detect changes in the length of, uh, length, down to 0.000000000000000001 meter or so, which is approximately the equivalent of one thousandth the width of a proton. This level of sensitivity should allow LIGO to detect the gravitational waves emitted by a pair of neutron stars colliding with each other anywhere within our local group of galaxies, but so far, LIGO hasn't come up with much.
What has come up with evidence for gravitational waves is a 75 year old optical telescope watching a pair of close-orbiting binary white dwarf stars. These stars complete one full orbit in under 13 minutes at less than a third of the distance between the Earth and the Moon (!), factors which work together to increase the intensity of the gravity waves that they emit. Producing gravity waves requires a significant amount of energy (enough to warp space itself, remember), and all that energy has to come from somewhere: Einstein figured that this gravitational radiation would suck up enough energy that binary stars orbiting each other would have their orbital period decrease, and that's exactly what astronomers are seeing.
With an optical telescope, we can measure how long it takes a pair of binary stars to complete one orbit by watching for changes in brightness when one of the stars eclipses the other one. Astronomers have been watching the system in question (which is about 3,000 light years from us) for about a year, and over that time, the length of the period between eclipses has shifted forwards by about six seconds. By next May, it'll be 20 seconds. And eventually, the stars will crash into each other. Sweet!
Of course, this is not a direct observation of gravity waves, but rather an observation of what gravity waves do. It's direct evidence for them, if you will. We're still waiting to measure a gravity wave itself, and for that, we'll have to hope that LIGO will eventually be able to pick something up.