Dispersivity (patchiness, filamentary structure, and so forth) in astrophysical objects is common; this dispersivity is associated with turbulence, which is partially the result of hydrodynamic instability. In many cases, "exchange" or "interchange" turbulence associated with unstable stratification in a gravitational field and bouyant forces is important The corresponding instabihty is called Rayleigh-Taylor, exchange, interchange, or sometimes gravitational instability; it is sometimes described in terms of the appearance of modes that arise, for example, in the case of flute instabihty, sausage instability, etc. In other cases, Richtmyer^Vleshkov instability occurs; this is brought about by initial velocity fluctuations. This review presents the most up-to-date information in this field of interest to astrophysicists, collected from various branches of science, and describes a number of astrophysical applications.