Offshore wind energy is currently the leading offshore renewable energy technology and plays an essential role in achieving a low carbon economy in Europe. Offshore wind turbines, as a result of the harsher offshore environment, suffer from high O&M costs, and as such a high overall LCOE. These higher O&M costs can be reduced by focusing on the most critical subassemblies of the OWT, by either improving the reliability of the subassembly or by better understanding the failure mechanism, and thus optimizing the O&M strategy. The power converter is identified as one of the most critical subassemblies as risk of the operation of the OWT in terms of maintainability and availability. The reliability of the power converter is heavily influenced by both its steady-state and its dynamic thermal behavior, and as such great attention will be paid to the literature related to the thermal behaviour of the power converter. This paper seeks to provide a comprehensive overview on how the typical mission profile of an OWT influences the thermal loading. The paper seeks to propose a comprehensive and up-to-date literature review related to the lifetime modelling of the power converter, and to highlight some of the main challenges yet to be tackled in the reliability analysis of the power converter, suggesting future areas of research.