The metal plastic forming process is typically subjected to multi-directional loading, whereas the uniaxial experiment can only reflect the mechanical response in one direction, and it is unable to characterize the deformation behavior of metal under multi-directional loading. In order to accurately describe the metal forming process, it is necessary to extend the research on the mechanical properties of sheet from uniaxial to biaxial or even multi-axial. In the actual forming process, such as stretching, forging and extrusion, the metal usually deforms under complex biaxial compressive stress. However, the influence of biaxial compressive stress state on the plastic deformation mechanism of metal is still unclear. Therefore, the mechanical response and corresponding microstructure evolution process of magnesium and aluminium alloys under biaxial compression loads were reviewed. First of all, the fixture and loading path used in the compression process were introduced. Subsequently, the selection of HCP metal twin types and variants during biaxial deformation was analyzed. The results demonstrate that the accumulation of macroscopic stress and strain facilitates the formation of twins during compression and secondary compression, and the secondary twin is correlated with the actual yield stress value of material. Finally, the commonly used constitutive models under biaxial compression were summarized, and the prospective development trends were discussed.