I will give a survey talk on the notion of modularity, a central theme leading the development of modern model theory. A model(=structure) or its theory having a suitable independence notion (such as simple, rosy, or o-minimal) is said to be modular if any two closed sets are independent over their intersection, sharing the dimensional property as a module or a vector space. The natural questions on modularity are whether a concrete infinite module (field, resp.) can be recovered in some 1st-order manner from a modular (non-modular, resp.) structure. For stable theories, Zilber and Hrushovski made pioneering works to answer the questions, and those play crucial roles in supplying spectacular applications of model theory to number theory. A considerable part of the results are recently extended to the context of simple theories. For o-minimal theories, the questions are fully answered without a constraint by Peterzil and Starchenko in mid 90s. Modularity also appears unexpectedly in algebraic geometry. For example, Faltings's solution to absolute Mordell-Lang says that the induced structure on the set of rational points of an elliptic curve is modular.