This will be a report on joint work with R. Cluckers and G. Comte. We shall present non-archimedean versions of the mean value theorem and the Yomdin-Gromov lemma, for certain classes of valued fields including (mathbb{Q}_p) and (mathbb{C} ((t))). These results are applied to get non-archimedean analogues of some classical results in diophantine geometry by Bombieri-Pila, Pila and Pila-Wilkie.