Magnesium alloys that are low density and have a high specific strength are widely utilized as lightweight structural materials. Due to their hexagonal close-packed crystal structure, plastic deformation in magnesium alloys is strongly limited in dislocation slip and mainly accommodated by deformation twinning, which results in distinct mechanical anisotropy and tension–compression asymmetry. This paper, centered on mechanism competition and microstructure regulation, systematically reviews the recent progress in the compressive mechanical responses of magnesium alloys. Key results reveal the cooperative and competitive mechanisms between slip and twinning, the significant controlling effects of temperature and strain rate on deformation behavior, and the effective design strategies of gradient and heterogeneous structures that achieve superior strength–ductility synergy. This review provides essential theoretical support for the development and performance optimization of high-performance magnesium alloys.