Solid oxide fuel cell (SOFC) is an efficient and environmentally friendly energy technology, used in distributed generation, transportation and residential systems. However, high-temperature operation, multi-physics coupling, and long-term degradation issues create significant control challenges. This paper reviews recent advances in SOFC control with key findings showing a shift from classical methods to intelligent systems. Parameter optimization currently employs algorithms such as the response surface method to obtain optimal control objectives. Fault diagnosis and performance prediction combine physical models with machine learning. Control strategies are evolving from traditional control toward intelligent control. Furthermore, application studies guide the tailoring of these advanced controllers to real-world settings. Despite these progresses, challenges remain due to insufficient control intelligence or weak fault tolerance. To address these gaps, this paper outlines two future research paths, including lifecycle digital twins for predictive health management, and explainable AI control for creating trustworthy systems by embedding physical constraints and ensuring decision transparency.