Gravity generally behaves itself. It keeps us anchored to the planet and when we drop things we know they'll fall down rather than up.
Alas, at its extremes — such as inside a black hole — the theory that describes gravity gets its knickers in a twist. It starts to spit out an infinite number of infinite answers that are impossible to resolve.
So something's amiss and we probably need another way to describe gravity. Gravity is described by General Relativity and the other three forces of nature are described by Quantum Theory. So the most obvious new way to describe gravity would be to lump it in with the other three forces and use quantum theory, but physicists have been trying to do this for nearly 100 years without success.
It would be useful if we could perform experiments on gravity at its extremes. The trouble is, if you built some experimental apparatus that harnessed enough energy to test gravity at its extremes, the experimental apparatus itself would turn into a black hole. That sort of thing pisses physicists off and probably breaches a number of health and safety regulations.
So where do we go from here?
In the article I link to, four physicists talk about how naughty gravity is.