Hydrogen energy is a promising renewable resource for the sustainable development of society. As a key member of the fuel cell (FC) family, the solid oxide fuel cell (SOFC) has attracted a lot of attention because of characteristics such as having various sources as fuel and high energy conversion efficiency, and being pollution-free. SOFC is a highly coupled, nonlinear, and multivariable complex system, and thus it is very important to design an appropriate control strategy for an SOFC system to ensure its safe, reliable, and efficient operation. This paper undertakes a comprehensive review and detailed summary of the state-of-the-art control approaches of SOFC. These approaches are divided into eight categories of control: proportional integral differential (PID), adaptive (APC), robust, model predictive (MPC), fuzzy logic (FLC), fault-tolerant (FTC), intelligent and observer-based. The SOFC control approaches are carefully evaluated in terms of objective, design, application/scenario, robustness, complexity, and accuracy. Finally, five perspectives are proposed for future research directions.