Plants have evolved different mechanisms to disperse from parent plants and improve germination to sustain their survival. The study of seed dispersal mechanisms, with the related structural and functional characteristics, is an active research topic for ecology, plant diversity, climate change, as well as for its relevance for material science and engineering. The natural mechanisms of seed dispersal show a rich source of robust, highly adaptive, mass and energy efficient mechanisms for optimized passive flying, landing, crawling and drilling. The secret of seeds mobility is embodied in the structural features and anatomical characteristics of their tissues, which are designed to be selectively responsive to changes in the environmental conditions, and which make seeds one of the most fascinating examples of morphological computation in Nature. Particularly clever for their spatial mobility performance, are those seeds that use their morphology and structural characteristics to be carried by the wind and dispersed over great distances (i.e. “winged” and “parachute” seeds), and seeds able to move and penetrate in soil with a self-burial mechanism driven by their hygromorphic properties and morphological features. By looking at their motion mechanisms, new design principles can be extracted and used as inspiration for smart artificial systems endowed with embodied intelligence. This mini-review systematically collects, for the first time together, the morphological, structural, biomechanical and aerodynamic information from selected plant seeds relevant to take inspiration for engineering design of soft robots, and discusses potential future developments in the field across material science, plant biology, robotics and embodied intelligence.