  A spin-polarized current transfers its spin-angular momentum to a local
magnetization, exciting current-induced magnetization dynamics. So far, most
studies in this field have focused on the direct effect of spin transport on
magnetization dynamics, but ignored the feedback from the magnetization
dynamics to the spin transport and back to the magnetization dynamics. Although
the feedback is usually weak, there are situations when it can play an
important role in the dynamics. In such situations, self-consistent
calculations of the magnetization dynamics and the spin transport can
accurately describe the feedback. This review describes in detail the feedback
mechanisms, and presents recent progress in self-consistent calculations of the
coupled dynamics. We pay special attention to three representative examples,
where the feedback generates non-local effective interactions for the
magnetization. Possibly the most dramatic feedback example is the dynamic
instability in magnetic nanopillars with a single magnetic layer. This
instability does not occur without non-local feedback. We demonstrate that full
self-consistent calculations generate simulation results in much better
agreement with experiments than previous calculations that addressed the
feedback effect approximately. The next example is for more typical spin valve
nanopillars. Although the effect of feedback is less dramatic because even
without feedback the current can induce magnetization oscillation, the feedback
can still have important consequences. For instance, we show that the feedback
can reduce the linewidth of oscillations, in agreement with experimental
observations. Finally, we consider nonadiabatic electron transport in narrow
domain walls. The non-local feedback in these systems leads to a significant
renormalization of the effective nonadiabatic spin transfer torque.
