  We study Grothendieck's dessins d'enfants in the context of the
$\mathcal{N}=2$ supersymmetric gauge theories in $\left(3+1\right)$ dimensions
with product $SU\left(2\right)$ gauge groups which have recently been
considered by Gaiotto et al. We identify the precise context in which dessins
arise in these theories: they are the so-called ribbon graphs of such theories
at certain isolated points in the Coulomb branch of the moduli space. With this
point in mind, we highlight connections to other work on trivalent dessins,
gauge theories, and the modular group.
