Features of the current spin–orbit induced magnetic dynamics in multilayer nanostructures with nonmagnetic heavy metal layers possessing by a strong spin–orbit interaction are studied. The spin Hall effect of the conversion of an incoming charge current into a transverse (with respect to the charge current) spin current impacting on the magnetic dynamics through a spin-transfer torque provides the excitation of the magnetic dynamics including magnetic precession and switching. The magneto-dynamic effect of a spin current pumping generation together with the inverse spin Hall effect of conversion of the spin current into the incoming charge current provide the influence of the magnetic dynamics on the incoming charge current. These feedforward and feedback between the incoming charge current and the magnetic dynamics can be the basis for the spin–orbit driven self-sustained and auto-oscillations of a magnetic order in ferro- and antiferromagnetics layers of the nanostructures. It is shown that the considered magnetic nanostructures can possess by properties of controlled microwave radiation attaining tens THz in the antiferromagnetic case.