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.