Polymeric tissue adhesives provide versatile materials for wound management and are widely used in a variety of medical settings ranging from minor to life-threatening tissue injuries. Compared to the traditional methods of wound closure (i.e., suturing and stapling), they are relatively easy to use, enable rapid application, and introduce minimal tissue damage. Furthermore, they can act as hemostats to control bleeding and provide a tissue-healing environment at the wound site. Despite their numerous current applications, tissue adhesives still face several limitations and unresolved challenges (e.g., weak adhesion strength and poor mechanical properties) that limit their use, leaving ample room for future improvements. Successful development of next-generation adhesives will likely require a holistic understanding of the chemical and physical properties of the tissue-adhesive interface, fundamental mechanisms of tissue adhesion, and requirements for specific clinical applications. In this review, we discuss a set of rational guidelines for design of adhesives, recent progress in the field along with examples of commercially available adhesives and those under development, tissue-specific considerations, and finally potential functions for future adhesives. Advances in tissue adhesives will open new avenues for wound care and potentially provide potent therapeutics for various medical applications.