Archimedean copulas have proven to be remarkably useful for modeling
dependence in a variety of settings. In this talk we will survey important
aspects of the theory of Archimedean copulas that make them well suited for
dependence modeling. We will discuss methods for constructing one and two
parameter families, dependence properties (e.g., tail dependence), applications
(e.g., extreme value theory, Schur-constant survival models), simulation
techniques, etc. Several open problems will also be presented.