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Metallic glasses have aroused considerable interest in the past decades because they exhibit fascinating properties. First, this article briefly outlines the mechanical, thermal properties and application of the metallic glasses. In addition, we focus on the dynamic mechanical relaxation behaviors, i.e. main (α) and secondary (β) relaxations, in metallic glasses. The mechanical relaxation behaviors are connected to the mechanical properties and physical properties in glassy materials. The main relaxation in glassy materials is related to the glass transition phenomenon and viscous flow. On the other hand, the β relaxation is linked to many fundamental issues in metallic glasses. In these materials relaxation processes are directly related to the plastic deformation mechanism. The mechanical relaxations, particularly, the β relaxation provides an excellent opportunity to design metallic glasses with desired physical and mechanical properties. We demonstrate the universal characteristics of main relaxation in metallic glasses. The phenomenological models and the physical theories are introduced to describe the main relaxation in metallic glasses. In parallel, we show the dependence of the α and β relaxations on the thermal treatments in metallic glasses. Finally, we analyze the correlation between the atomic mobility and the thermo-mechanical treatments in metallic glasses. On the one hand, the atomic mobility in metallic glasses is reduced by physical aging or crystallization. On the other hand, the atomic mobility in metallic glass is enhanced by deformation (i.e. compression and cold rolling). Importantly, to analyze the atomic mobility in amorphous materials, a physical theory is introduced. This model invokes the concept of quasi-point defects, which correspond to the density fluctuations in the glassy materials. [ABSTRACT FROM AUTHOR]