Efficient extraction of wind energy is a complex, multidisciplinary process. This paper examines common objectives used in wind turbine optimization problems. The focus is not on the specific optimized designs, but rather on understanding when certain objectives and constraints are necessary, and what their limitations are. Maximizing annual energy production, or even using sequential aero/structural optimization, is shown to be significantly suboptimal compared to using integrated aero/structural metrics. Minimizing the ratio of turbine mass to annual energy production can be effective for fixed rotor diameter designs, as long as the tower mass is estimated carefully. For variable-diameter designs, the predicted optimal diameter may be misleading. This is because the mass of the tower is a large fraction of the total turbine mass, but the cost of the tower is a much smaller fraction of overall turbine costs. Minimizing the cost of energy is a much better metric, though high fidelity in the cost modeling is as important as high fidelity in the physics modeling. Furthermore, deterministic cost of energy minimization can be inadequate, given the stochastic nature of the wind and various uncertainties associated with physical processes and model choices. Optimization in the presence of uncertainty is necessary to create robust turbine designs.