I plan to survey the development of the concept of multiplica- tivity, from its appearance in the definition of Poisson-Lie groups (as the compatibility condition of a bivector with the group multiplication) to the multiplicativity of tensors and forms on Lie groupoids and their infinitesimal counterparts on Lie algebroids. If time permits, I shall outline the results of Jotz-Sti ́enon-Xu (2016) on multiplicative generalized complex structures on Lie groupoids.