I introduced the notion of matched pairs of groups 20 years ago, motivated by W. M. Singer's work on Hopf algebra extensions. This notion was later applied to quantum group theory by S. Majid, and its cohomology theory was studied by A. Masuoka and I. Hofstetter with its origin in G. Kac's work on group extensions in late 60's. Recently, two groups of algebraists, one is J. Lu, M. Yan and Y. Zhu, and the other is P. Etingof, T. Schedler and A.. Soloviev, have contributed to the notion and found some interesting applications in set-theoretical solutions of the Yang-Baxter equation. The first group has found a new construction of quasi-triangular structures on bi-smash product Hopf algebras. I will survey these topics on matched pairs of groups.