Wind energy is currently the fastest-growing energy source in the world, with a concurrent growth in demand for the expertise of engineers and researchers in the wind energy field. There are still many unsolved challenges in expanding wind power, and there are numerous problems of interest to systems and control researchers. In this paper, we first review the basic structure of wind turbines and then describe wind turbine control systems and control loops. Of great interest are the generator torque and blade pitch control systems, where significant performance improvements are achievable with more advanced systems and control research. We describe recent developments in advanced controllers for wind turbines and wind farms, and we also outline many open problems in the areas of modeling and control of wind turbines.