The current understanding of radiation tolerance of Silicon Photomultipliers (SiPMs) is reviewed. Radiation damage in silicon sensors is briefly introduced, surface and bulk effects are separately addressed. Results on the operation of irradiated SiPMs with X-ray, gamma, electron, proton and neutron sources are presented. The most critical effect of radiation on SiPMs is the increase of dark count rate, which makes it impossible to resolve signals generated by a single photon from the noise. Methods to characterize irradiated SiPMs after their single photo-electron resolution is lost are discussed. Due to the important similarity in the operation below the breakdown voltage, also studies on radiation damage of avalanche photo-diodes (APD) are reviewed. Finally, ideas are presented on how to approach the development of radiation hard SiPMs in the future.