Operations and maintenance (O&M) of floating offshore wind turbines (FOWTs) require regular inspection activities to predict, detect, and troubleshoot faults at high altitudes and in harsh environments such as strong winds, waves, and tides. Their costs typically account for more than 30% of the lifetime cost due to high labor costs and long downtime. Different inspection methods, including manual inspection, permanent sensors, climbing robots, remotely operated vehicles (ROVs), and unmanned aerial vehicles (UAVs), can be employed to fulfill O&M missions. The UAVs, as an enabling technology, can deal with time and space constraints easily and complete tasks in a cost-effective and efficient manner, which have been widely used in different industries in recent years. This study provides valuable insights into the existing applications of UAVs in FOWT inspection, highlighting their potential to reduce the inspection cost and thereby reduce the cost of energy production. The article introduces the rationale for applying UAVs to FOWT inspection and examines the current technical status, research gaps, and future directions in this field by conducting a comprehensive literature review over the past 10 years. This paper will also include a review of UAVs’ applications in other infrastructure inspections, such as onshore wind turbines, bridges, power lines, solar power plants, and offshore oil and gas fields, since FOWTs are still in the early stages of development. Finally, the trends of UAV technology and its application in FOWTs inspection are discussed, leading to our future research direction.