Statistical distributions for the amplitude, intensity, and phase of randomly scattered sound are important in a variety of problems involving noise characterization, detection, communication, beamforming, and remote sensing. This paper discusses some recent progress in modeling the distributions of scattered sound and the situations to which they apply. In particular, several extensions to the gamma distribution are described: the compound gamma for signals that have been scattered with randomly varying strength, the variance gamma for the complex products (covariances and cross spectra) between pairs of sensors, and the compound variance gamma for signals at pairs of sensors with varying scattering strength. Furthermore, a new joint amplitude-phase distribution, termed the phase-modulated Rice, is described, which is appropriate for signals that are scattered by inhomogeneities spanning a broad range of spatial scales as occurs in atmospheric turbulence. This distribution employs the basic (unmodulated) Rice distribution for scattering by relatively small (Fresnel-zone scale) turbulent eddies, while the phase is modulated with a von Mises distribution to represent the impact of relatively strong large-scale turbulence.