In this talk I will present a classification of tame forms of annuli, i.e. those analytic spaces defined over a discretely valued field that become annuli after finite tamely ramified extension (obtained in collaboration with Lorenzo Fantini). The proof of this result combines the theory of semi-affinoid spaces and their models with the study of automorphisms of finite order of analytic curves. After having introduced such tools, I will explain how our result can be applied to resolution of singularities of surfaces and semi-stable reduction of curves in a tame context. Finally, I will discuss a strategy to generalize this approach to the wildly ramified case, building on techniques coming from the theory of lifting automorphisms of curves from characteristic p to characteristic zero.