In clinical practice, tissue adhesives have emerged as an alternative tool for wound treatments due to their advantages in ease of use, rapid application, less pain, and minimal tissue damage. Since most tissue adhesives are designed for internal use or wound treatments, the biodegradation of adhesives is important. To endow tissue adhesives with biodegradability, in the past few decades, various biodegradable polymers, either natural polymers (such as chitosan, hyaluronic acid, gelatin, chondroitin sulfate, starch, sodium alginate, glucans, pectin, functional proteins, and peptides) or synthetic polymers (such as poly(lactic acid), polyurethanes, polycaprolactone, and poly(lactic-co-glycolic acid)), have been utilized to develop novel biodegradable tissue adhesives. Incorporated biodegradable polymers are degraded in vivo with time under specific conditions, leading to the destruction of the structure and the further degradation of tissue adhesives. In this review, we first summarize the strategies of utilizing biodegradable polymers to develop tissue adhesives. Furthermore, we provide a symmetric overview of the biodegradable polymers used for tissue adhesives, with a specific focus on the degradability and applications of these tissue adhesives. Additionally, the challenges and perspectives of biodegradable polymer-based tissue adhesives are discussed. We expect that this review can provide new inspirations for the design of novel biodegradable tissue adhesives for biomedical applications.