In recent years, polymer-based tissue adhesives (TAs) have been developed as an alternative to sutures to close and seal incisions or wounds owing to their ease of use, rapid application time, low cost, and minimal tissue damage. Although significant research is being conducted to develop new TAs with improved performances using different strategies, the applications of TAs are limited by several factors, such as weak adhesion strength and poor mechanical properties. Therefore, the next-generation advanced TAs with biomimetic and multifunctional properties should be developed. Herein, we review the requirements, adhesive performances, characteristics, adhesive mechanisms, applications, commercial products, and advantages and disadvantages of proteins- and synthetic polymer-based TAs. Furthermore, future perspectives in the field of TA-based research have been discussed.