This talk concerns the inverse source scattering problem for acoustic, elastic, and electromagnetic waves. The first part is to discuss the inverse random source problems where 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 second part addresses the stability of the inverse source problems. We show that increasing stability can be achieved by using the Dirichlet boundary data at multiple frequencies.