The utility of polarized electron beams for precision electroweak studies is
described. Parity violating Moller scattering asymmetries in e-e- --> e-e- are
discussed. Effects of electroweak radiative corrections and the running
sin^2(theta_W(Q^2)) are reviewed. The sensitivity of E158 (a fixed target e-e-
experiment at SLAC) and future e-e- collider studies to ``new physics'' is
briefly outlined.Comment: Updated Fig.