Wind energy is a rapidly growing field of renewable energy and as such, intensive scientific and societal interest has been already attracted. Research on wind turbine structures has been mostly focused on the structural analysis, design and/or assessment of wind turbines mainly against normal (environmental) exposures while, so far, only marginal attention has been spent on considering extreme natural hazards that threat the reliability of the lifetime-oriented wind turbine's performance. Especially, recent installations of numerous wind turbines in earthquake prone areas worldwide (e.g., China, USA, India, Southern Europe and East Asia) highlight the necessity for thorough consideration of the seismic implications on these energy harnessing systems. Along these lines, this state-of-the-art paper presents a comparative survey of the published research relevant to the seismic analysis, design and assessment of wind turbines. Based on numerical simulation, either deterministic or probabilistic approaches are reviewed, since they have been adopted to investigate the sensitivity of wind turbines' structural capacity and reliability in earthquake-induced loading. The relevance of seismic hazard for wind turbines is further enlightened by available experimental studies, being also comprehensively reported through this paper. The main contribution of the study presented herein is to identify the key factors for wind turbines' seismic performance while important milestones for ongoing and future advancement are emphasized.