The main experimental studies of the spin properties of two-dimensional electron systems by means of electrically detectable electron spin resonance are discussed. The key aspects of spin resonance are considered, including the detection mechanism, the anisotropy of spin splitting, and the influence of hyperfine and spin-orbit interactions on the physics of spin resonance. Particular attention is paid to systems with strong electron-electron interactions formed in various AlAs/AlGaAs and ZnO/MgZnO semiconductor heterostructures. It is in such material systems that a whole series of unique physical phenomena related to spin have been observed. The prospects of electron spin resonance in two-dimensional systems are discussed.