The review starts by highlighting the significance of nuclear power plants in the contemporary world, especially its indispensable role in the global efforts to reduce CO2 emissions. Then, it describes the impact of irradiation on the microstructure and mechanical properties of reactor structural materials. The main part provides the reader with a thorough overview of crystal plasticity models developed to address the irradiation effects so far. All three groups of the most important materials are included. Namely, the Zr alloys used for fuel cladding, austenitic stainless steels used for reactor internals, and ferritic steels used for reactor pressure vessels. Other materials, especially those considered for construction of future fission and fusion nuclear power plants, are also mentioned. The review also pays special attention to ion implantation and instrumented nanoindentation which are common ways to substitute costly and time-consuming neutron irradiation campaigns.