The propagation of electromagnetic waves through a random assembly of electric and magnetic dipole scatterers is considered. The results may be taken as the leading term of the solution for more general multipole scatterers. Multiple forward scattering and the coherent-wave approach of J. B. Keller are compared. To the first order, the theories differ only in that they predict different wave polarizations. Particular attention is given to the case in which the distribution of scatterer orientations is axisymmetric. It is found that this case can be treated as propagation through an assembly of uniformly aligned equivalent scatterers. The application of these results to propagation through rain is discussed briefly.