In March 2004, the European Space Agency launched the ambitious Rosetta mission, which will visit a comet named 67P/Churyumov-Gerasimenko. Rosetta will orbit the comet and then land on it, the first time this will have ever been attempted.
Comets are basically lumps of rocks frozen together in a matrix of ice made of water, hydrogen, and other things that would normally be a gas at room temperature. When they get near the Sun, those ices sublimate (turn from solid to gas), and the comet nucleus (the solid part) gets enveloped in a fuzzy ball of gas (called the coma). Studying the comet when it's near the Sun, then, makes it hard to study the solid part.
So duh, study it when it's far away from the Sun. But that's a problem because comets are dinky and faint, and when they're far from the Sun they are really hard to observe. You need a big 'scope.
Hey, the Very Large Telescope has an 8 meter mirror! Is that big enough?
Click it for a higher-res version. The tiny dot in the center (I added green crosshairs; they used a thin circle that's hard to see) is the comet in May 2006 when it was 680 million kilometers from the Sun. That's out past Jupiter! Observations over time revealed the comet is rotating; its brightness goes up and down. It takes about 12.8 hours to spin once, and the brightness variation indicates its an irregular shape, which is expected. Halley's comet has a nucleus shaped like a potato, so there you go.
They also found a dust trail from the comet, probably from bits ejected over millennia that have spread out over that time:
The dust trail is the fuzzy part extending from the nucleus to the lower right (the picture is a time exposure, so stars and everything streak in the same direction, making the dust trail easier to see since it points off to the side). Mind you, the comet was 680 million kilometers away when that image was taken. In astronomy, you'd better believe bigger is better, and the VLT has 8 meters of bignitude. That's a lot of 'scope and it can see very faint stuff.
All this information is pretty useful when you're trying to land a probe on the comet... and you're attempting this when the probe is 600 million kilometers away! That'll happen in 2014, and when it does, the images will be HAWESOME*. I'm sure we'll learn a lot about comets, and that's good, because they're cool, and they can hit the Earth, and learning more about them will help us understand how to prevent that, but c'mon, honestly: the images will be HAWESOME.
I can't wait!
* OK, I know you'll ask, so here. NSFW words. Hat tip to my ManCrush Wil Wheaton for that link, BTW.