Nature benefits from a progressive evolution over millions of years, always adapting and finding individual solutions for common problems. Hence, a pool of diverse and efficient solutions exists that may be transferable to technical systems. Biomimetics or bio-inspiration has been used as a design approach for decades, revolutionizing products and processes throughout various industries. Thus, multiple examples can also be found in the space sector, since many characteristics found in biological organisms are also essential for space systems like response-stimuli adaptability, robustness and lightweight construction, autonomy and intelligence, energy efficiency, and self-repair or healing capabilities. This review focuses on biomimetics within the field of aerospace engineering and summarizes existing bio-inspired concepts such as drilling tools (wood wasp ovipositor drilling), telescopes (lobster eye optics), or gasping features (gecko feet adhesion capabilities) that have already been conceptualized, partially tested, and applied within the space sector. A multitude of biological models are introduced and how they may be applicable within the space environment. In particular, this review highlights potential bio-inspired concepts for dealing with the harsh environment of space as well as challenges encountered during rocket launches, space system operations and space exploration activities. Moreover, it covers well-known and new biomimetic concepts for space debris removal and on-orbit operations such as space-based energy production, servicing and repair, and manufacture and assembly. Afterwards, a summary of the challenges associated with biomimetic design is presented to transparently show the constraints and obstacles of transferring biological concepts to technical systems, which need to be overcome to achieve a successful application of a biomimetic design approach. Overall, the review highlights the benefits of a biomimetic design approach and stresses the advantage of biomimetics for technological development as it oftentimes offers an efficient and functional solution that does not sacrifice a system’s reliability or robustness. Nevertheless, it also underlines the difficulties of the biomimetic design approach and offers some suggestions in how to approach this method.