Recent developments in the theory of multimode random lasers

We review recent extensions of semiclassical multimode laser theory to open systems with overlapping resonances and inhomogeneous refractive index. An essential ingredient of the theory are biorthogonal quasimodes that describe field decay in an open passive system and are used as a basis for lasing modes. We discuss applications of the semiclassical theory, as well as other experimental and numerical results related to random lasing with mode competition.