  We present a theory of the spin Hall magnetoresistance (SMR) in multilayers
made from an insulating ferromagnet F, such as yttrium iron garnet (YIG), and a
normal metal N with spin-orbit interactions, such as platinum (Pt). The SMR is
induced by the simultaneous action of spin Hall and inverse spin Hall effects
and therefore a non-equilibrium proximity phenomenon. We compute the SMR in
F$|$N and F$|$N$|$F layered systems, treating N by spin-diffusion theory with
quantum mechanical boundary conditions at the interfaces in terms of the
spin-mixing conductance. Our results explain the experimentally observed spin
Hall magnetoresistance in N$|$F bilayers. For F$|$N$|$F spin valves we predict
an enhanced SMR amplitude when magnetizations are collinear. The SMR and the
spin-transfer torques in these trilayers can be controlled by the magnetic
configuration.
