Charge shot noise, the intrinsic fluctuations in the electrical current resulting from the statistics of the arrival of discrete electronic charges, was predicted more than a century ago2 and has been an invaluable tool for examining the mechanism of charge transport and the nature of current-carrying excitations.3-8 A noise in a nonequilibrium angular momentum current analogous to shot noise seen in charge flow is expected, since the carrier of angular momentum, magnon, also has a discrete nature. In this dissertation, I mainly studied the nonequilibrium noise due to fluctuations in angular momentum current. We first explored the possibility of identifying the effect of spin accumulation on charge shot noise in Pt/h-BN/Au tunnel junctions, where a flicker noise is caused by the thermally excited dynamic defects in the h-BN layer itself. The defect density is on the order of a few per square micron. We also detected a spin Seebeck voltage noise in structures designed to measure the longitudinal spin Seebeck effect in yttrium iron garnet (YIG) on gadolinium gallium garnet (GGG). Measurements have shown indications at low temperatures of a contribution to the spin Seebeck voltage noise in the inverse spin Hall detector that is present when the magnetization of the underlying YIG/GGG is oriented transverse to the Pt wire and absent when the magnetization is oriented along the Pt wire.