Wind power curves play important roles in wind power forecasting, wind turbine condition monitoring, estimation of wind energy potential and wind turbine selection. In practice, it is a challenging task to produce reliable wind power curves from raw wind data due to the presence of outliers formed in unexpected conditions, e.g., wind curtailment and blade damage. This paper comprehensively reviews wind power curve modeling techniques from the perspective of modeling processes, i.e., wind data analyses, wind data preprocessing and various wind power curve models. Moreover, the performances of many popular power curve models are studied in different seasons and different wind farms. The results show that no universal wind power curve model can always perform better than other models under any environmental conditions. In general, there are three factors that affect the final wind power curves: data filtering approaches; wind power curve models; and choice of optimization strategies (especially the method applied to construct objective functions). However, there is no guarantee that all outliers will be removed from the raw wind data. Consequently, designing robust regression models or constructing robust objective functions may be two effective ways to obtain accurate power curves in the presence of outliers. The above two strategies depend largely on the error characteristics of power curve modeling. While it is often observed that the error distribution of the power curve modeling may be asymmetric, few researchers have considered this trait when building wind power curves. Therefore, this paper proposes several strategies that focus on designing asymmetric loss functions and developing robust regression models with asymmetric error distributions. Models that benefit from these characteristics may be more suitable for power curve modeling tasks and are more likely to produce better wind power curves.