Concrete is a relatively cheap material and easy to be cast into variously shaped structures. Its good shielding properties against neutrons and gamma-rays, due to its intrinsic water content and relatively high-density, respectively, make it the most widely used material for radiation shielding also. Concrete is so chosen as biological barrier in nuclear reactors and other nuclear facilities where neutron sources are hosted. Theoretical formulas are available in nuclear engineering manuals for the optimum thickness of shielding for radioprotection purposes; however they are restricted to one-dimensional problems; besides the basic empirical constants do not consider radiation damage effects, while its long-term performance is crucial for the safe operation of such facilities. To understand the behaviour of concrete properties, it is necessary to examine concrete strength and stiffness, water behavior, volume change of cement paste, and aggregate under irradiated conditions. Radiation damage process is not well understood yet and there is not a unified approach to the practical and predictive assessment of irradiated concrete, which combines both physics and structural mechanics issues. This paper provides a collection of the most distinguished contributions on this topic in the past 50 years. At present a remarkable renewed interest in the subject is shown.