With the continuous growth of wind power integration into the electrical grid, accurate wind power forecasting is an important component in management and operation of power systems. Given the challenging nature of wind power forecasting, various methods are presented in the literature to improve wind power forecasting accuracy. Among them, combining different techniques to construct hybrid models has been frequently reported in the literature. Decomposition-based models are a family of hybrid models that firstly decompose the wind speed/power time series into relatively more stationary subseries, and then build forecasting models for each subseries. In this paper, we present a comprehensive review of decomposition-based wind forecasting methods in order to explore their effectiveness. Decomposition-based hybrid forecasting models are classified into different groups based on the decomposition methods, such as, wavelet, empirical mode decomposition, seasonal adjust methods, variational mode decomposition, intrinsic time-scale decomposition, and bemaola galvan algorithm. We discuss decomposition methods in the context of alternative forecasting algorithms, and explore the challenges of each method. Comparative analysis of various decomposition-based models is also provided. We also explore current research activities and challenges, and identify potential directions for future research on this subject.