The review is devoted to the analysis of the formation and evolution of flows of astrophysical objects of various nature. The members of these streams are destructible astronomical objects: comets, asteroids, planets, stars, star clusters, galaxies. Almost all of the indicated flows are now observed. The conditions for the destruction of the original objects, the formation and dissipation of these flows are considered. Numerical models of streams generated by comets, asteroids, stars and their clusters, galaxies in their clusters are constructed, and the evolution of these streams on the Hubble time scale is traced.