In this talk, inverse random source problems for acoustic and electromagnetic waves will be introduced. The unknown random source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical pseudo-differential operator. The well-posedness of the direct problem in the distribution sense as well as the regularity of the solution is given for the case that the random source is extremely rough and should be interpreted as a distribution. The strength of the random source, involved in the principal symbol of its covariance operator, is shown to be uniquely determined by a single realization of the magnitude of the wave field averaged over the frequency band with probability one