What are copulas?

The notion of copula was introduced by A. Sklar in 1959, when answering a question raised by M. Fréchet about the relationship between a multidimensional probability function and its lower dimensional margins. At the beginning, copulas were mainly used in the development of the theory of probabilistic metric spaces. Later, they were of interest to define nonparametric measures of dependence between random variables, and since then, they began to play an important role in probability and mathematical statistics. In this paper, a general overview of the theory of copulas will be presented. Some of the main results of this theory, various examples, and some open problems will be described