The results of recent theoretical studies of features of superconducting states in hybrid structures whose properties are significantly determined by the spin–orbit effects have been reported. The two main phenomena appearing in such systems in the presence of additional spin splitting caused either by the Zeeman effect in a magnetic field or by the exchange field: (i) the generation of spontaneous currents and (ii) the appearance of topologically nontrivial superconducting phases. It has been shown that the spin–orbit coupling can be a key mechanism that allows implementing new inhomogeneous phase structures, in particular, the so-called “phase batteries.” The effect of geometric factors on the properties of topologically nontrivial superconducting states has been analyzed. New types of topological transitions in vortex states of Majorana wires have been proposed.