Let K be a complete discrete valuation field of mixed characteristic (0,p). If f:Y --> P^1 is a branched G-Galois cover of the projective line over K, and p | #G, then f often does not have good reduction, and we must be content with a stable model. The speaker has used this stable model to help understand arithmetic fundamental groups (in particular, to analyze fields of moduli of branched covers). In the case that G = Z/p^n and f is a three-point cover, there are also applications of Colmez and Coleman-McCallum (not yet understood by the speaker) to number theory, including generalizations of the Chowla-Selberg formula relating periods of abelian varieties to special values of L-functions. . We will review the basics of the stable model, not assuming any knowledge. Then we will sketch the computation of the stable model of any Z/p^n three- point cover. This was done by Coleman-McCallum (1988) for p > 2, but our method involves far less guesswork, and is also applicable to the case p=2. Underlying our method is a generalization of a "vanishing cycles formula" due to Raynaud.