Riemann, Dedekind, Hecke, Artin, Selberg, Ruelle,... the list of names associated to "zeta functions" is long, nearly as long the list of objects to which zeta functions have been attached, ranging from number fields over riemannian manifolds to partially ordered sets, dynamical systems and — finally — groups.

This talk will try to give a conceptual answer to the question "what is a zeta function" by "categorifying" Dirichlet series, and to look at some recurring themes connecting various kinds of zeta functions.