  When a strongly disordered system of interacting quantum dipoles is locally
excited, the excitation relaxes on some (potentially very long) timescale. We
analyze this relaxation process, both for electron glasses with strong Coulomb
interactions - in which particle-hole dipoles are emergent excitations - and
for systems (e.g., quantum magnets or ultracold dipolar molecules) made up of
microscopic dipoles. We consider both energy relaxation rates ($T_1$ times) and
dephasing rates ($T_2$ times), and their dependence on frequency, temperature,
and polarization. Systems in both two and three dimensions are considered,
along with the dimensional crossover in quasi-two dimensional geometries. A
rich set of scaling laws is found.
