The processes that control irradiation creep are dependent on the temperature and the rate of production of freely migrating point defects, affecting both the microstructure and the mechanisms of mass transport. Because of the experimental difficulties in studying irradiation creep, many different hypothetical models have been developed that either favour a dislocation slip or a mass transport mechanism. Irradiation creep mechanisms and models that are dependent on the microstructure, which are either fully or partially mechanistic in nature, are described and discussed in terms of their ability to account for the in-reactor creep behaviour of various nuclear reactor core materials. A rate theory model for creep of Zr-2.5Nb pressure tubing in CANDU reactors incorporating the as-fabricated microstructure has been developed that gives good agreement with measurements for tubes manufactured by different fabrication routes having very different microstructures. One can therefore conclude that for Zr-alloys at temperatures < 300 °C and stresses < 150 MPa, diffusional mass transport is the dominant creep mechanism. The most important microstructural parameter controlling irradiation creep for these conditions is the grain structure. Austenitic alloys follow similar microstructural dependencies as Zr-alloys, but up to higher temperature and stress ranges. The exception is that dislocation slip is dominant in austenitic alloys at temperatures < 100 °C because there are few barriers to dislocation slip at these low temperatures, which is linked to the enhanced recombination of irradiation-induced point defects.