Plasma and dust are key ingredients of the universe, and in larger astrophysical systems the gravitational and electrostatic forces can become comparable, thus prompting a careful revision of stationary configurations of self-gravitating dusty plasmas. An overview of some physically acceptable models is given, with applications to relevant structures in space and astrophysical plasmas. For those cases where explicit solutions can be obtained, the scales over which the system is inhomogeneous are of the order of the Jeans lengths, determined in the usual way by studying local perturbations of a uniform equilibrium.