  We survey some aspects of the theory of the integrated density of states
(IDS) of random Schroedinger operators. The first part motivates the problem
and introduces the relevant models as well as quantities of interest. The proof
of the existence of this interesting quantity, the IDS, is discussed in the
second section. One central topic of this survey is the asymptotic behavior of
the integrated density of states at the boundary of the spectrum. In
particular, we are interested in Lifshitz tails and the occurrence of a
classical and a quantum regime. In the last section we discuss regularity
properties of the IDS. Our emphasis is on the discussion of fundamental
problems and central ideas to handle them. Finally, we discuss further
developments and problems of current research.
