The “dessins d'enfants” were introduced by A. Grothendieck in Esquisse d'un programme. They allow to visualize the finite (topological, analytical or algebraic, it amounts to the same thing) coverings of the complex projective line, with $0$, $1$ et $\infty $ removed. Such a covering has a unique model over $\overline {\mathbf {Q}}$ and is determined by the following data : a finite set with two permutations. To study the action of $\mathrm {Gal}(\overline {\mathbf {Q}}/\mathbf {Q})$ on these objects, and their models over the ring of algebraic integers are two central questions of the subject.