  We summarize recent results initiating spectral analysis on pseudo-Riemannian
locally symmetric spaces $\Gamma \backslash G/H$, beyond the classical setting
where $H$ is compact (e.g. theory of automorphic forms for arithmetic $\Gamma$)
or $\Gamma$ is trivial (e.g. Plancherel-type formula for semisimple symmetric
spaces).
