This paper gives a review of the advantages offered by an integral representation using diffracting component waves in solving wave propagation problems, deterministic as well as stochastic, in multiscale media. The component waves are constructed in such a way that they account for the diffraction on local inhomogeneities. As a result, the method presented here describes propagation effects which pertain to nonzero values of the wave parameter of the local inhomogeneities embedded in the smoothly inhomogeneous background medium. The technique involves in a natural way the concepts of complex rays and complex caustics. In random problems the method describes the influence of diffraction by local random inhomogeneities on the field also in the near-caustic areas. The method given is particularly suitable for solving HF wave propagation problems in the disturbed ionosphere. ¿ American Geophysical Union 1996