It is shown that a vertically vibrated binary granular gas mixture of light and heavy particles can segregate (in the presence of gravity) in such a way that the bottom and top layers are composed mostly of light particles, even if all other parameters (including size) are the same for both species. The corresponding concentration profile possesses certain universal properties. It is also shown that such mixtures can segregate when the only difference between the species is the value of the coefficient of restitution. These findings follow from a set of hydrodynamic equations for granular gas mixtures which we derived from the pertinent Boltzmann equation. The above results comprise the second part of this article, the first part of which is devoted to a brief and somewhat biased review of the main physical properties of granular gases. This includes their (generic) tendency to coagulate into clusters and other micro- and macrostructures. A fundamental property of granular materials in general, and granular gases in particular, is the lack of scale separation; an explanation and some consequences are presented. The answer to the basic question of whether the dynamics of granular gases lends itself to description by (appropriate) hydrodynamic equations seems to be positive, though some restrictions apply.