This article provides a survey of recently emerged methods for wind turbine control. Multivariate control approaches to the optimization of power capture and the reduction of loads in components under time-varying turbulent wind fields have been under extensive investigation in recent years. We divide the related research activities into three categories: modeling and dynamics of wind turbines, active control of wind turbines, and passive control of wind turbines. Regarding turbine dynamics, we discuss the physical fundamentals and present the aeroelastic analysis tools. Regarding active control, we review pitch control, torque control, and yaw control strategies encompassing mathematical formulations as well as their applications toward different objectives. Our survey mostly focuses on blade pitch control, which is considered one of the key elements in facilitating load reduction while maintaining power capture performance. Regarding passive control, we review techniques such as tuned mass dampers, smart rotors, and microtabs. Possible future directions are suggested.