For something that might not even exist, black holes do a whole lot of work for modern physics. These regions of compact mass--so dense that not even light can escape their gravitational fields--are a major underpinning of general relativity, and inform much of what we think we understand about how galaxies work. It's a lot to ask of a phenomenon that we've never actually seen.
Then again seeing a black hole is, by definition, a difficult idea to execute. The absence of reflected light makes black holes invisible, and the fact that the really interesting supermassive ones hide obscured at the center of galaxies compounds the problem. You would need to build a telescope the size of planet Earth to capture an image of a black hole. And that's exactly what Sheperd Doeleman, assistant director of MIT's Haystack Observatory, and his colleagues at the Event Horizon Telescope (EHT) are trying to do.