Multiaxial　fatigue　damage　behavior　and　life　prediction　is　related　to　the　service　safety　of　metal　structures　under　complex　loading　condition,　which　has　received　great　attention　in　the　field　of　science　and　engineering.　The　general　process　of　fatigue　testing　and　fatigue　behavior　research　under　multiaxial　low-cycle　and　high-cycle　fatigue　are　summarized.　The　influence　of　multiaxial　nonproportional　loading　on　fatigue　behavior　of　low-cycle　and　high-cycle　fatigue　is　emphatically　discussed.　The　effect　of　nonproportional　loading　on　low-cycle　fatigue　hardening　behavior　and　fatigue　life　of　materials　is　different　due　to　the　loading　path,　loading　load　and　material　type.　The　effect　of　nonproportional　loading　on　fatigue　behavior　of　low-cycle　and　high-cycle　fatigue　and　damage　mechanism　is　also　different.　Uniaxial　constitutive　relation　can　be　extended　to　the　field　of　multiaxial　fatigue　by　introducing　nonproportional　factor,　correcting　cyclic　strength　coefficient　or　equating　the　strain　of　multiaxial　loading　to　uniaxial　strain.　The　multiaxial　fatigue　life　prediction　models　based　on　stress,　strain,　energy,　the　critical　plane　and　critical　plane　strain　energy　density　methods　are　reviewed.　Some　multiaxial　fatigue　life　prediction　approaches　which　contain　energy　term　in　fatigue　damage　parameters　have　been　applied　to　a　wide　range　of　multiaxial　low-cycle　and　high-cycle　fatigue　life.　The　fatigue　life　of　notched　parts　can　be　predicted　based　on　the　multiaxial　damage　parameters　combined　with　the　local　stress-strain　method,　stress　gradient　method,　stress　field　intensity　method　and　critical　distance　method.　©　2021　Journal　of　Mechanical　Engineering.