  We formulate a general microscopic approach to spin-orbit torques in thin
ferromagnet/heavy-metal bilayers in linear response to electric current or
electric field. The microscopic theory we develop avoids the notion of spin
currents and spin-Hall effect. Instead, the torques are directly related to a
local spin polarization of conduction electrons, which is computed from
generalized Kubo-St\v{r}eda formulas. A symmetry analysis provides a one-to-one
correspondence between polarization susceptibility tensor components and
different torque terms in the Landau-Lifshitz-Gilbert equation for
magnetization dynamics. The spin-orbit torques arising from Rashba or
Dresselhaus type of spin-orbit interaction are shown to have different
symmetries. We analyze these spin-orbit torques microscopically for a generic
electron model in the presence of an arbitrary smooth magnetic texture. For a
model with spin-independent disorder we find a major cancelation of the
torques. In this case the only remaining torque corresponds to the
magnetization-independent Edelstein effect. Furthermore, our results are
applied to analyze the dynamics of a Skyrmion under the action of electric
current.
