Various formulations of problems in the statistical theory of diffraction and wave propagation are discussed: excitation of fields by random sources, diffraction of partially coherent waves, diffraction of waves by bodies having random shapes or positions, and diffraction and propagation of waves in a randomly inhomogeneous medium. For each of these types of problem, physical problems from acoustics, radio astronomy, radiophysics, optics, and other branches of physics are given as examples, and the methods (mostly approximate ones) most widely used for solving them are indicated. Among the problems discussed are those of the diffraction content of the radiation transport equation and the back scattering enhancement effect observed in the diffraction of waves by small bodies immersed in a randomly irregular medium. Examples of statistical problems of mixed type are also given.