We do not have a final answer to the question of why galaxies choose a particular internal mass distribution. Here we examine whether the distribution is set by thermodynamic equilibrium (TE). Traditionally, TE is discarded for a number of reasons including the inefficiency of two-body collisions to thermalize the mass distribution in a Hubble time, and the fact that the mass distribution maximizing the classical Boltzmann–Gibbs entropy is unphysical. These arguments are questionable. In particular, when the Tsallis entropy that describes self-gravitating systems is used to define TE, the mass distributions that result (i.e., the polytropes) are physically sensible. This work spells out this and other arguments for TE and presents the polytropes and their properties. It puts forward empirical evidence for the mass distribution observed in galaxies to be consistent with polytropes. It compares polytropes with Sérsic functions and it shows how the DM halos resulting from cosmological numerical simulations become polytropes when efficient collisions are allowed. It also discusses pathways to thermalization bypassing two-body collisions. It finally outlines future developments including deciphering whether or not DM particles collide efficiently.