The dynamic control of the metasurface opens up a vital technological approach for the development of multifunctional integrated optical devices. The magnetic field manipulation has the advantages of sub-nanosecond ultra-fast response, non-contact, and continuous adjustment. Thus, the magnetically controllable metasurface has attracted significant attention in recent years. This study introduces the basic principles of the Faraday and Kerr effect of magneto-optical (MO) materials. It classifies the typical MO materials according to their properties. It also summarizes the physical mechanism of different MO metasurfaces that combine the MO effect with plasmonic or dielectric resonance. Besides, their applications in the nonreciprocal device and MO sensing are demonstrated. The future perspectives and challenges of the research on MO metasurfaces are discussed.