The basic concepts of the theory of mass superflows in a superfluid are presented. The stability of such flows with respect to the creation and growth of linear defects (superfluid vortices), the relationship between superflows and the existence of long-range order, and the possible occurrence of persistent flows in one- and two-dimensional systems are discussed. Some analogs of the mass superflows in a superfluid are also examined: spin superflows in magnetically ordered systems having an easy-plane anisotropy and the current states of a Bose condensate of electron-hole pairs. The physical meaning of such ``flows'' is discussed, and a theory for their stability is derived from the calculated probability for the creation of the linear defects which are analogs of superfluid vortices. There is a discussion of the applicability of the theory of spin superflows to several experiments on the magnetic properties of the A phase of superfluid helium-3 and to a possibility which follows from this theory: that domain walls might be generated in the interior of a sample of an easyplane magnetically ordered material and that the motion of these walls might be controlled by fields applied to the surface of the sample.