  Exact and/or rigorous results are reviewed for the Ising and XY/Villain spin
glasses in finite dimensions, such as the exact energy, correlation identities
and a functional relation between the distribution functions of ferromagnetic
and spin glass order parameters. This last relation is useful to prove that the
phase space is not complex on a line in the phase diagram. The spin wave theory
neglecting periodicity is shown to give exact results for the Villain model on
a line in the phase diagram. Implications of this fact on the
renormalization-group results for the random-phase XY/Villain model in two
dimensions are discussed.
