We present a large class of homogeneous 2-nondegenerate CR-manifolds $M$, both of hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CR-equivalence between domains $U$, $V$ in $M$ extends to a global real-analytic CR-automorphism of $M$. We show that this class contains $G$-orbits in Hermitian symmetric spaces $Z$ of compact type, where $G$ is a real form of the complex Lie group $Aut{\left(Z\right)}^0$ and $G$ has an open orbit that is a bounded symmetric domain of tube type.

We survey some recent results on holomorphic or formal mappings sending real submanifolds in complex space into each other. More specifically, the approximation and convergence properties of formal CR-mappings between real-analytic CR-submanifolds will be discussed, as well as the corresponding questions in the category of real-algebraic CR-submanifolds.