We consider the characteristic of eigenvalue distributions called the integrated density of states. This characteristic is an analogue of the Weyl counting function and can be defined for a large of selfadjoint differential and matrix operators with random and almost periodic coefficients. We discuss its definition, ergodic properties, smoothness, asymptotic formulae on various parts of the spectrum and results interpolating between two most studied es of operators : differential and finite-difference operators with random coefficients and random matrices with dependent identically distributed entries.