Jumping is a locomotion strategy widely evolved in both invertebrates and vertebrates. In addition to terrestrial animals, several aquatic animals are also able to jump in their specific environments. In this paper, the state of the art of jumping robots has been systematically analyzed, based on their biological model, including invertebrates (e.g., jumping spiders, locusts, fleas, crickets, cockroaches, froghoppers and leafhoppers), vertebrates (e.g., frogs, galagoes, kangaroos, humans, dogs), as well as aquatic animals (e.g., both invertebrates and vertebrates, such as crabs, water-striders, and dolphins). The strategies adopted by animals and robots to control the jump (e.g., take-off angle, take-off direction, take-off velocity and take-off stability), aerial righting, land buffering, and resetting are concluded and compared. Based on this, the developmental trends of bioinspired jumping robots are predicted.