  In this article, we define and study the class of simple transitive
$2$-representations of finitary $2$-categories. We prove a weak version of the
classical Jordan-H\"older Theorem where the weak composition subquotients are
given by simple transitive $2$-representations. For a large class of finitary
$2$-categories we prove that simple transitive $2$-representations are
exhausted by cell $2$-representations. Finally, we show that this large class
contains finitary quotients of $2$-Kac-Moody algebras.
