Electromagnetic radiation of high energy electrons (positrons) and electron-positron pair production by gamma-quanta in crystals and their simulations are reviewed. In particular, the following topics are discussed. Strong field synchrotron type radiation, pair production and accompanying polarization and spin effects. Electron and positron radiation in crystal undulators and thin crystals. Electron and positron radiation under the multiple volume reflection in one crystal and axial alignment of PWO crystal. Specific features of incoherent scattering and radiation of high energy particles in oriented crystals.
