In this talk, our recent progress will be discussed on inverse source problems for the stochastic wave equations. I will present a new model for the random source, which is assumed to be a microlocally isotropic Gaussian random field such that its covariance operator is a classical pseudo-differential operator. The well-posedness and regularity of the solution will be addressed for the direct problem. For the inverse problem, it is shown that the principal symbol of the covariance operator can be uniquely determined by the high frequency limit of the wave field at a single realization. I will also highlight some ongoing and future projects in the inverse random potential and medium problems.