This review covers the major advances achieved in the studies of EM wave propagation in turbulent media for the last two decades with the focus on new physical problems, effects and formalisms., The greatest attention has been directed to the problem of strong fluctuations of intensity. The theoretical results of this treatise include the path integration technique, the predominant correlation method, the two-scale method, the phase approximation in Huygens' method, the hybrid approach to scattering from small inhomogeneities in the presence of large ones, the theory of coherent channels in backscattering, and the concept of partially determinate processes and fields.New physical effects described in the review include the rise of the coherence radius in intermittent turbulence, backscatter enhancement, doubling the variance of phase, incidence angles, group delay, and frequency shifts in the double passage of waves through turbulent media, the residual scintillation effect, the long correlation effect in backscattering, the partial reversal of wavefronts in turbulent media, the magic cap effect in reflection from phase conjugated mirrors, the strong localization of UHF radic waves in stochastic tropospheric waveguides, the effect of penetration in caustic shadow%, and enhanced translucence. New fields of experimental research have been outlined, such as scattering from vegetation and snow covers, and coherent structures in tuibulences, and new objects of theoretical analysis have been elicited: random dislocations of wsvefronts, fractal^ and critical wave phenomena, and the predictability of random fields.