Jumping in planthopper and froghopper insects is propelled by a catapult-like mechanism requiring mechanical storage of energy and its quick release to accelerate the hind legs rapidly. To understand the functional biomechanics involved in these challenging movements, the internal skeleton, tendons and muscles involved were reconstructed in 3-D from confocal scans in unprecedented detail. Energy to power jumping was generated by slow contractions of hind leg depressor muscles and then stored by bending specialised elements of the thoracic skeleton that are composites of the rubbery protein resilin sandwiched between layers of harder cuticle with air-filled tunnels reducing mass. The images showed that the lever arm of the power-producing muscle changed in magnitude during jumping, but at all joint angles would cause depression, suggesting a mechanism by which the stored energy is released. This methodological approach illuminates how miniaturized components interact and function in complex and rapid movements of small animals.