Niels Bohr and Einstein think about it
In physics, there are often different equations for the same phenomenon, but you can usually do a little algebra and show that the different equations actually come from the same source. This is considered good and normal.
So, it's a lot more than a bit embarrassing that the two most important ideas in modern physics — quantum mechanics, which are used to describe teeny tiny things, and General Relativity, which is used to describe big-ass things — have no connection at all. They don't match. To go from one to the other, you have to close one book, put it away, and open another.
For example, Einstein showed that gravity is really just geometry. Mass warps space, and so objects tend to slide down the geometrical warps that other objects create, moving closer together. When we look at this, it looks like gravitational attraction. Unfortunately, quantum mechanics thinks of gravity as an effect generated when masses pass little particles back and forth between them. These ideas are no more compatible to physicists than they are to me or you.
Generally, the conflict can just be ignored, but in certain cases, the two worlds collide. When you want to talk about teeny tiny spaces with HUGE gravitational fields — like black holes, or the Big Bang — you're in real trouble. You need physics that hasn't been invented yet — you need "quantum gravity" or a "Grand Unified Theory". People are working on some interesting ideas (like string theory) in trying to develop this new physics, but it's not clear whether anyone is on the right track or not.
Check your local bookstore for a good article in the July 2005 Sky and Telescope, describing experiments designed to help break the log jam. In terms of the margin of error, quantum mechanics has been confirmed with a lot more precision than General Relativity has. If Einstein's work could be confirmed way, way down to the umpteenth digit, and if this work revealed some difficulties with the theory, it might help unravel the curtain separating the physics of the very large and the very small. Astronomy is at the forefront of the effort, hence the article in Sky and Telescope.