A review of physical processes related to disorder in spinorbit coupling in two-dimensional electron gas is presented. We begin with the analysis of the sources of the randomness in the spinorbit coupling in semiconductor structures and establish the corresponding Hamiltonian. We demonstrate that in multiple quantum wells electronelectron interaction is a source of a time-dependent randomness in the spinorbit coupling, additional to that provided by the static disorder. The spin relaxation of free and localized in quantum dots electrons, memory effects and spin relaxation enhancement in magnetic field, and spin manipulation and spin current injection by external electric fields in the structures where the spinorbit coupling is random, are considered. In addition, we study spin relaxation in single-layer graphene, which provides an excellent example of a system with disordered spinorbit coupling.