This is a survey article on ordinary differential equations over
nonarchimedean fields based on the author's lecture at the 2015 Simons
Symposium on nonarchimedean and tropical geometry. Topics include: the
convergence polygon associated to a differential equation (or a connection on a
curve); links to the formal classification of differential equations
(Turrittin-Levelt); index formulas for de Rham cohomology of connections;
ramification of finite morphisms; relations with the Oort lifting problem on
automorphisms of curves. The appendices include some new technical results and
an extensive thematic bibliography.Comment: v2: final refereed version; one appendix withdrawn, other minor
correction
