<p>Fractional-order systems have emerged as a novel and significant research direction in control science and engineering. These systems have gained increasing attention in academia due to their enhanced capability in accurately modeling real-world physical phenomena. The growing interest in this field is further driven by the inherent presence of various system uncertainties, external disturbances, and nonlinear characteristics, which stem from multiple factors including component aging, environmental variations in temperature and pressure, and modeling inaccuracies. Consequently, the robustness analysis and synthesis of uncertain fractional-order systems have become crucial research focuses within the discipline of robust control. This paper aims to give an exhaustive review on the robust control of continuous time fractional-order systems including robust stability, robust stabilization, robust performance control and robust nonlinear control. Various robust analysis methodologies and control objectives are comparatively discussed for fractional-order systems. Potential open problems to enhance to the effectiveness and application of the robust control of fractional-order systems are also given.</p>