Fields of generalized power series are central objects in Model Theory and Algebra. They play an important role in: - ordered algebraic structures (Hausdorff's lexicographic orders, Hahn's groups), - non-standard models of arithmetic (integer parts), - non-standard models of o-minimal expansions of the reals (exponentiation), - model theory of valued fields (saturated and recursively saturated models, Ax-Kochen principles), - real algebraic geometry (non-archimedean real closed fields), - valuation theory (Kaplansky's embedding theorem), - differential algebra (ordered differential fields, Hardy fields), - difference algebra (automorphism groups), - transcendental number theory (Schanuel's conjectures). I will give an overview of my work with these fascinating objects in the last decade.