Well, from what I've encountered, it's concerned with Riemann surfaces and conformal mappings between Riemann surfaces. It seems to draw together a lot of areas of mathematics: classical complex analysis, Banach manifolds, discrete geometry, algebraic topology.
No one at the university I'm attending is doing research in this area. I know of a few books (Ahlfors' lectures on quasiconformal mappings; Gardiner's two books), I'm just wondering if there are any others.