Naturally derived polymeric biomaterials, such as collagens, silks, elastins, alginates, and fibrins are utilized in tissue engineering due to their biocompatibility, bioactivity, and tunable mechanical and degradation kinetics. The use of these natural biopolymers in biomedical applications is advantageous because they do not release cytotoxic degradation products, are often processed using environmentally-friendly aqueous-based methods, and their degradation rates within biological systems can be manipulated by modifying the starting formulation or processing conditions. For these reasons, many recent in vivo investigations and FDA-approval of new biomaterials for clinical use have utilized natural biopolymers as matrices for cell delivery and as scaffolds for cell-free support of native tissues. This review highlights biopolymer-based scaffolds used in clinical applications for the regeneration and repair of native tissues, with a focus on bone, skeletal muscle, peripheral nerve, cardiac muscle, and cornea substitutes.