Electron and hole $g$ factors in semiconductors and nanostructures (Review)

We present a review of experimental and theoretical studies of the spin response of charge carriers to an external magnetic field in bulk semiconductors and semiconductor nanostructures. The linear response is quantitatively characterized by the magnitude of the electron or hole g factor. Various experimental methods for measuring the electron g factor are considered, beginning with historical works and including modern research. A detailed analysis of theoretical methods for calculating the electron and hole g factors in bulk semiconductors and nanostructures of various shapes also includes fundamental work from previous years and the present time.