Locomotion techniques employed by different biological animals are extremely diverse and fascinating from an engineering point of view. The explorations of planets such as Mars, Titan, Europa, Enceladus with the use of aerial, terrestrial, and underwater rovers are gaining significant interest from academia, industry, planetary scientists, robotic engineers, and international space agencies around the globe. This article presents an overview of the existing state-of-the-art investigations on recently developed flapping foil propulsion of UAVs (unmanned aerial vehicles) and AUVs (autonomous underwater vehicles) for the exploration of Earth's oceans and other terrestrial bodies such as Mars, Jupiter's moon Europa, and Saturn's moon Titan. The use of flapping foils further advances into Martian Atmospheres in the form of insect-inspired micro aerial vehicles working at low Reynolds numbers. The development of aerial vehicles mimicking insect flapping is essential in low Reynolds number environments to generate sufficient lift and thrust for carrying out future Mars missions. The Cassini mission to Titan, Voyage mission, and other flyby missions to Europa found that liquid atmosphere exists on the subsurface of Europa and on the surface of Titan in the form of liquid methane lakes. The ice-covered ocean under the Europa surface is analogous to the Antarctic ice. The developments of autonomous surface ships and underwater vehicles for the exploration of the planets in cryogenic conditions are discussed with suitable biomimetic propulsion systems. The design methodology, hydrodynamic stability, and resistance estimation in cryogenic atmospheres are presented which can act as a benchmark for future missions. © 2020 The Author(s)