Nature is a substantial repository for various kinds of aquatic, terrestrial, and wind-borne plants and animals adapting extensively to sustain life on earth's different environmental conditions. The organisms or structures of these natural creatures possess extraordinary properties or functionalities through well-organizing usually weak biopolymers and bioinorganic structures, which provide good examples to emulate their mechanical and structural characteristics in materials innovations and discoveries. This review collectively investigates the studies of the structures and mechanical properties of some representative fauna and flora with robust mechanical properties and the corresponding bioinspired materials with mimicking structures and mechanical properties. By learning from the natural structures with robust mechanical properties, bioinspired materials and composites with superior mechanical performance to the constituent materials have been designed and fabricated. Via this study, there is hope to draw some principles for designing innovative materials with extraordinary properties from existing common materials by learning from nature. It is expected that the understanding of the extraordinary natural mechanical properties and the robust bioinspired materials can provide some insights into the design of novel materials and composites.