Wind farm control design is a recently new area of research that has rapidly become a key enabler for the development of large wind farm projects and their safe and efficient connection to the power grid. A comprehensive review of the intense research conducted in this area over the last 10 years is presented. Part I reviews control system concepts and structures and classifies them depending on their main objective (i.e. to maximise power production or to provide grid services. The work and key findings in each paper are discussed in detail with particular emphasis on the turbine side. Additionally, the review contributes to the existing reviews on the area by providing an elegant classification between model testing and control approaches. Areas where significant work is still needed are also discussed. In Part II, a thorough review on aerodynamic wind farm models for control design purposes is provided.