A complete surveillance strategy for wind turbines requires both the condition monitoring (CM) of their mechanical components and the structural health monitoring (SHM) of their load-bearing structural elements (foundations, tower, and blades). Therefore, it spans both the civil and mechanical engineering fields. Several traditional and advanced non-destructive techniques (NDTs) have been proposed for both areas of application throughout the last years. These include visual inspection (VI), acoustic emissions (AEs), ultrasonic testing (UT), infrared thermography (IRT), radiographic testing (RT), electromagnetic testing (ET), oil monitoring, and many other methods. These NDTs can be performed by human personnel, robots, or unmanned aerial vehicles (UAVs); they can also be applied both for isolated wind turbines or systematically for whole onshore or offshore wind farms. These non-destructive approaches have been extensively reviewed here; more than 300 scientific articles, technical reports, and other documents are included in this review, encompassing all the main aspects of these survey strategies. Particular attention was dedicated to the latest developments in the last two decades (2000–2021). Highly influential research works, which received major attention from the scientific community, are highlighted and commented upon. Furthermore, for each strategy, a selection of relevant applications is reported by way of example, including newer and less developed strategies as well.