This review will present the latest research related to the production and application of spider silk and silk-based materials in reconstructive and regenerative medicine and tissue engineering, with a focus on musculoskeletal tissues, and including skin regeneration and tissue repair of bone and cartilage, ligaments, muscle tissue, peripheral nerves, and artificial blood vessels. Natural spider silk synthesis is reviewed, and the further recombinant production of spider silk proteins. Research insights into possible spider silk structures, like fibers (1D), coatings (2D), and 3D constructs, including porous structures, hydrogels, and organ-on-chip designs, have been reviewed considering a design of bioactive materials for smart medical implants and drug delivery systems. Silk is one of the toughest natural materials, with high strain at failure and mechanical strength. Novel biomaterials with silk fibroin can mimic the tissue structure and promote regeneration and new tissue growth. Silk proteins are important in designing tissue-on-chip or organ-on-chip technologies and micro devices for the precise engineering of artificial tissues and organs, disease modeling, and the further selection of adequate medical treatments. Recent research indicates that silk (films, hydrogels, capsules, or liposomes coated with silk proteins) has the potential to provide controlled drug release at the target destination. However, even with clear advantages, there are still challenges that need further research, including clinical trials.