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Proton exchange membrane fuel cell (PEMFC) is a promising future power source, which uses hydrogen energy to generate electricity with the byproduct of water. In general, PEMFC includes several strongly coupled subsystems with high nonlinearity and complex dynamic processes. Therefore, proper control strategies are crucial for a reliable and effective PEMFC operation. This paper aims to carry out a comprehensive and systematic overview of state-of-the-art PEMFC control strategies. Based on a thorough investigation of 180 literatures, these control strategies are classified into nine main categories, including proportional integral derivative (PID) control, adaptive control (APC), fuzzy logic control (FLC), robust control, observer-based control, model predictive control (MPC), fault tolerant control (FTC), optimal control and artificial intelligence control. Furthermore, a comprehensive evaluation and detailed summary of their control deigns, objectives, performance, applications, advantages/disadvantages, complexity, robustness and accuracy are conducted thoroughly. Finally, five valuable and insightful perspectives/recommendations are proposed for future research. [Display omitted] • Summarize nine groups of PEMFC system control strategies. • Control complexity, robustness, and accuracy are summarized and evaluated. • Present the advantages/disadvantages of all methods. • Five invaluable and insightful perspectives/recommendations are proposed. [ABSTRACT FROM AUTHOR]