This talk concerns the inverse source scattering problems for acoustic, elastic, and electromagnetic waves. The inverse random source problems will be discussed. The sources are assumed to be random functions driven by the additive white noise. The inverse problems are to determine statistical properties of the random sources from the boundary measurement of the radiated random wave fields. The stability will be addressed for the deterministic counterpart of the inverse source problems. We show that increasing stability can be achieved by using the Dirichlet boundary data at multiple frequencies.