The replacement of fossil fuels by intermittent renewable energy sources is transforming energy systems world-wide. A significant part of the future electricity demand will be supplied by offshore renewable energy, especially wind, but emerging technologies such as wave and tidal energy also offer great potential. However, the ability of offshore renewable energy systems – and of power systems and the societies that dependent on them – to cope with hazards such as extreme weather and metocean events is not well known. Resilience has become an increasingly important concept in the study of energy systems, as it addresses not only vulnerability to hazards but also the ability to recover from disturbances. Weather extremes are responsible for a majority of electricity blackouts, and the resilience of power systems to extreme weather hazards has long been an established field of research. However, the topic has not been examined to the same extent for offshore renewable energy systems; for marine energy technologies in particular, resilience is a novel concept. In the present study, we review the research that has been published starting from a discussion on the general resilience concept and its applicability for power systems. By identifying knowledge gaps and outlining directions for future research needed to build resilient and renewable energy systems, the paper contributes to several of the Sustainable Development Goals (SDGs). In particular, the paper supports the goals of affordable and clean energy (SDG 7), climate action (SDG 13), and sustainable cities and communities (SDG 11).