the theory of drinfeld modules is remarkably similar to the theory of abelian varieties, but their local monodromy behaves differently and is poorly understood. in this talk i will present a research program which aims to fully describe this monodromy. the cornerstone of this program is a ``z-adic'' variant of grothendieck's l-adic monodromy theorem. \\ \\ the talk is aimed at a general audience of number theorists and arithmetic geometers. no special knowledge of monodromy theory or drinfeld modules is assumed.