In this chapter, we formulate a general conjecture regarding the discrete spectrum on standard pseudo-Riemannian locally homogeneous spaces XΓ = Γ\G/H from the perspective of the unitary representation theory of the real reductive Lie group G. In contrast to the classical Riemannian context, the natural projection Γ\G → XΓ has a noncompact fiber H. This implies that the Hilbert space L2(XΓ) cannot be realized in the Hilbert space L2(Γ\G), on which the group G acts as a unitary representation by right translations. Nevertheless, we anticipate that the discrete spectrum for intrinsic differential operators on the standard quotients XΓ is connected to H-distinguished irreducible unitary representations of G. We formulate a conjecture for both type I and type II spectrum in this regard. We support the conjecture with some evidence, including the example of standard 3-dimensional anti-de Sitter manifolds, using transfer maps.