I’ll describe some results of Nopal-Coello, on the dynamics of quadratic rational maps over a complete and algebraically closed ultrametric field. The first result is a tricothomy: Every quadratic rational map is either simple, has an invariant Herman domain or is uniformly hyperbolic. Somewhat surprisingly, these cases are distinguished by the number N of repelling fixed points of the rational map. They correspond to N = 1, 2 and 3, respectively. The second result is that a quadratic rational map can have at most 1 Herman domain.