In this talk we overview the historical development of Quantum Groups, starting from the theory of quantum integrable systems, formalized by Vladimir Drinfeld and Michio Jimbo inside the category of Hopf algebras. We briefly discuss the bicrossproducts introduced by Shahn Majid. 

We sketch some selected applications. Particular classes of quantum groups had already been used in the study of the quantum Yang-Baxter equation and quantum inverse scattering method, developed by the Leningrad School (Ludwig Faddeev, Leon Takhtajan, Evgeny Sklyanin, Nicolai Reshetikhin and Vladimir Korepin). On the other hand, bicrossproducts served the search for self-dual objects as an approach to quantum gravity. 

We also discuss the analytic version of Quantum Groups, first appeared in the work of Polish school leading by S. L. Woronowicz. We briefly comment on the later development by J. Kustermans and S. Vaes.