Surface flashover is a devastating electronic avalanche along the gas–solid interface when a high electric field is applied, which is a potential issue that threatens the safe operations of advanced power electronic, electrical, and spacecraft applications. However, the underlying physical mechanisms for surface flashover development are still under investigation owing to the complex charge transport processes through the gas phase, solid phase, and gas–solid interface. In this study, the history of surface flashover theory in the last 50 years is introduced, and several key questions are reviewed from the perspective of the competing mechanisms of charge transport: the role of each phase in a surface flashover, the origin of surface charging, and effects of traps in solid on surface flashover. Then, some suggestions involve charge transport processes in each phase, and their correlations are put forward, and a predictable ‘charge transport competitive flashover model’ is proposed by clarifying the competing mechanisms of charge transport processes through multiple phases. This study summarises the history and hot topics of physical mechanisms of surface flashover proposed based on classic and recent progress and offers promising routes for developing a more precise surface flashover theory and improving surface flashover performances.