The relaxation dynamics of metallic glasses, as one of the most challenging issues, is complex. The relaxation, including α relaxation, slow β relaxation, and fast β relaxation, occurs at different temperatures. Taking advantage of the microscopic atomic information of simulation, the characteristics and mechanisms of these three typical relaxations were summarized to discuss their influence on mechanical properties of metallic glasses. Recent progresses on dynamical, structural, and physical mechanisms by simulation method were discussed. This review is beneficial to understand the nature of glass and to establish the dynamics-structure-property relationship of glassy materials.