The main goal of this paper is to establish the present state of the art for wind farm control. The control area that will be focused on is the mechanical/aerodynamic part, which includes the wind turbines, their power production, fatigue and wakes affecting neighbouring wind turbines. The sub-objectives in this area of research are as follows: (i) maximizing the total wind farm power production; (ii) following a reference for the total wind farm active power; and (iii) doing this in a manner that minimizes fatigue loading for the wind turbines in the farm. Each of these sub-objectives is discussed, including the following important control issues: choice of input and output, control method and modelling used for controller design and simulation. The available literature from industry is also considered. Finally, a conclusion is presented discussing the established results, open challenges and necessary research.