  Current-induced spin torques in layered magnetic heterostructures have many
commonalities across broad classes of magnetic materials. These include not
only collinear ferromagnets, ferrimagnets, and antiferromagnets, but also more
complex noncollinear spin systems. We develop a general Lagrangian-Rayleigh
approach for studying the role of dissipative torques, which can pump energy
into long-wavelength magnetic dynamics, causing dynamic instabilities. While
the Rayleigh structure of such torques is similar for different magnetic
materials, their consequences depend sensitively on the nature of the order
and, in particular, on whether there is a net magnetic moment. The latter
endows the system with a unipolar switching capability, while magnetically
compensated materials tend to evolve towards limit cycles, at large torques,
with chirality dependent on the torque sign. Apart from the ferromagnetic and
antiferromagnetic cases, we discuss ferrimagnets, which display an intricate
competition between switching and limit cycles. As a simple case for
compensated noncollinear order, we consider isotropic spin glasses, as well as
a scenario of their coexistence with a collinear magnetic order.
