Given a p-cyclic cover C -> P^1 of the projective line over a p-adic field K, one would like to describe the semi-stable reduction. C. Lehr and M. Matignon have recently given a new characterization of the semi-stable reduction, including some results on the finite monodromy (i.e. the minimal field extension K'/K over which C attains semi-stable reduction). This talk (the first of two) will be an exposition of this work, following the recent paper "Wild monodromy and automorphisms of curves" (arXiv:math.AG/0412294).