The use of wind power, a pollution-free and renewable form of energy, to generate electricity has attracted increasing attention. However, intermittent electricity generation resulting from the random nature of wind speed poses challenges to the safety and stability of electric power grids when wind power is integrated into grids on large scales. Therefore, accurate forecasting of wind speed and wind power (WS/WP) has gradually taken on a key role in reducing wind power fluctuations in system dispatch planning. With the development of artificial intelligence technologies, especially deep learning, increasing numbers of deep learning-based models are being considered for WS/WP forecasting due to their superior ability to deal with complex nonlinear problems. This paper comprehensively reviews the various deep learning technologies being used in WS/WP forecasting, including the stages of data processing, feature extraction, and relationship learning. The forecasting performance of some popular models is tested and compared using two real-world wind datasets. In this review, three challenges to accurate WS/WP forecasting under complex conditions are identified, namely, data uncertainties, incomplete features, and intricate nonlinear relationships. Moreover, future research directions are summarized as a guide to improve the accuracy of WS/WP forecasts. • Review and compare deep feature extraction models in terms of computation cost. • Review and discuss various single and hybrid deep models for relationship learning. • Present an overview of intelligent optimizers for model configuration determination. • Summarize challenges and future research directions in wind energy forecasting.