This paper discusses the application of the new concept of spatial time-frequency distribution (STFD), and more generally the spatial arbitrary joint-variable distribution (SJVD), to key array signal processing problems including blind source separations and high resolution direction finding of narrowband and broadband sources with stationary and nonstationary temporal characteristics. The STFD can be formulated based on the widely used class of time-frequency distributions, namely Cohen's class, or it can be devised by incorporating other classes of quadratic distributions, such as the: Hyperbolic class and the Affine class. The paper delineates the fundamental offerings of STFDs, presents three examples of array signal processing using the localization properties of time-frequency distributions of the impinging signals, and summarizes recent contributions in this area.