Owing to concern over the environment, there is much interest in renewable sources of electrical power generation, of which one of the most promising is wind power. Wind turbines exploit this energy source to directly generate electrical power. There are essentially two types of wind turbines, namely constant speed and variable speed machines. The purpose of this paper is to investigate the dynamics of variable speed wind turbines and determine suitable models to support the control design task. A basic but widely used dynamic representation of variable speed wind turbines and the corresponding models of the control plant dynamics are initially discussed. More detailed, yet still simple models, are derived separately for the rotor aerodynamics, the drive-train dynamics and the power generation unit dynamics before being combined to form the complete model of the wind turbine dynamics. The resulting combined model, in addition to supporting the control design task, enables the extent, to which the basic models adequate represent the wind turbine, to be assessed. It is concluded that the basic models of variable speed wind turbines are not adequate and do not exhibit all the relevant aspects of the dynamics necessary to support the control design.