A　bioinspired　jumping　robot　has　a　strong　ability　to　overcome　obstacles.　It　can　be　applied　to　the　occasion　with　complex　and　changeable　environment,　such　as　detection　of　planet　surface,　postdisaster　relief,　and　military　reconnaissance.　So　the　bioinspired　jumping　robot　has　broad　application　prospect.　The　jumping　process　of　the　robot　can　be　divided　into　three　stages:　takeoff,　air　posture　adjustment,　and　landing　buffer.　The　motivation　of　this　review　is　to　investigate　the　research　results　of　the　most　published　bioinspired　jumping　robots　for　these　three　stages.　Then,　the　movement　performance　of　the　bioinspired　jumping　robots　is　analyzed　and　compared　quantitatively.　Then,　the　limitation　of　the　research　on　bioinspired　jumping　robots　is　discussed,　such　as　the　research　on　the　mechanism　of　biological　motion　is　not　thorough　enough,　the　research　method　about　structural　design,　material　applications,　and　control　are　still　traditional,　and　energy　utilization　is　low,　which　make　the　robots　far　from　practical　applications.　Finally,　the　development　trend　is　summarized.　This　review　provides　a　reference　for　further　research　of　bioinspired　jumping　robots.