The objective of this paper is an improved understanding of the physics of the aeroelastic motion of wind turbine blades in order to improve the numerical models used for their design. Two- and three-dimensional Navier-Stokes calculations of the flow around a wind turbine airfoil using the k - omega SST and Detached Eddy Simulation (DES) turbulence models, as well as an engineering semiempirical dynamic stall model, are conducted. The computational results are compared to the experimental results that are available for both the static airfoil and the pitching airfoil. It is shown that the Navier-Stokes simulations can reproduce the main characteristic features of the flow. The DES model seems to be able to reproduce most of the details of the unsteady aerodynamics. Aerodynamic work computations indicate that a plunging motion of the airfoil can become unstable.