Marine operations required to transfer technicians and equipment represent a significant proportion of the total cost of offshore wind. The profile of sites being considered for floating offshore wind farms (FOWFs), e.g., further from the shore and in harsher environments, indicates that these costs need to be assessed by taking into account the maintenance requirements and restricted weather windows. There is an immediate need to investigate the potential use of robotic systems in the wind farm's operations and maintenance (O&M) activities, to reduce the need for costly manned visits. The use of robotic systems can be critical, not only to replace repetitive activities and bring down the levelised cost of energy but also to reduce the health and safety risks by supporting human operators in performing the desired inspections. This paper provides a review of the state of the art in the applications of robotics for O&M of FOWFs. Emerging technology trends and associated challenges and opportunities are highlighted, followed by an outline of the agenda for future research in this domain.