Black holes, being black holes, aren't the easiest things to take pictures of. Not only are they black (absorbing nearly all the light that falls on them) , they also tend to be small, far away, and surrounded by things that are very very bright. The only way we're going to get a good look at one from here is to use as large and sensitive a radio telescope as we possibly can, and the largest radio telescope you can possibly build on Earth is, well, a radio telescope the size of Earth itself.
This sounds a little nuts, but astronomers want to build a virtual Earth-sized radio telescope by linking together a bunch of different radio telescopes all over the world. They're not going to try to fill in all the gaps (which ould involve covering most of the planet with antennas), but they don't have to: thanks to a technique called Very Long Baseline Interferometry, an array of widely separated telescopes that are carefully synchronized can emulate (in some respects) one single telescope the size of the maximum distance between the farthest apart telescopes in the array.
Astronomers say that if they can get this thing to work, they'll point it at the center of our galaxy (26,000 light years away) and try to snap the first ever photo of the gigantic black hole (with a mass of about 4 million suns) that we're pretty sure lives there. What we want to see, specifically, is the outline of the black hole's event horizon, which should be a perfect circle in a radio image. If it's not, then Einstein's general theory of relativity is going to have some explaining to do.
We've already seen plenty of visual evidence for black holes; for example, here's a Hubble pic of what's assumed to be a black hole at the core of a galaxy:
Of course, we're not seeing the black hole itself in this image: we're seeing all the energy that the stuff falling into the black hole is giving off. The radio image, on the other hand, will be the first ever of the event horizon of a black hole proper.
Astronmers are meeting this week to plan out how the project is going to work, and they say that this new system, called the Event Horizon Telescope, could start producing pictures within five years.