In this paper, we review the radiation damage issues caused by displacement damage in silicon sensors operating in the harsh radiation environments of high energy physics experiments. The origin and parameterization of the changes in the macroscopic electrical sensor properties such as depletion voltage, leakage current, and charge collection efficiency as a function of fluence of different particles, annealing time, and annealing temperature are reviewed. The impact of impurities in the silicon base crystal on these changes is discussed, revealing their effects on the degradation of the sensor properties. Differences on how segmented and nonsegmented devices are affected and how device engineering can improve radiation hardness are explained and characterization techniques used to study sensor performance and the electric field distribution inside the irradiated devices are outlined. Finally, recent developments in radiation hardening and simulation techniques using technology computer-aided design modeling are given. This paper concludes with radiation damage issues in presently operating experiments and gives an outlook of radiation-hardened technologies to be used in the future upgrades of the Large Hadron Collider and beyond.