Recently, polymeric bioadhesives have become known as promising alternatives to sutures, staples, and wires. Traditional wound closure techniques are time-consuming to apply and cause additional tissue damage. In instances of large-scale hemorrhage or minimally invasive laparoscopic surgery, sutures are impractical to apply. Alternatively, newly developed bioadhesives are polymers that can be dripped or sprayed over superficial or internal injuries, solidifying in situ to form a seal that apposes tissue or arrests bleeding over large areas. This review will outline the main categories of polymers that have been investigated for these applications. The chemistry, mechanisms of adhesion, and advantages and limitations of each category will be described. In addition, needs for next-generation adhesives in tissue engineering will be discussed. For the repair of certain load-bearing areas of the body, such as cartilage and the intervertebral disc, scaffold adhesion is necessary for anchoring the scaffold in place and providing adequate transmission of forces. Researchers continue developing new formulations that exhibit improved biocompatibility, strength, elasticity, and degradability. These advances promise to improve clinical outcomes by enhancing bleeding control and wound healing. In the long term, bioadhesives will play an important role in making orthopedic and musculoskeletal tissue engineering clinically feasible.