  For $S$ a contractive analytic operator-valued function on the unit disk
${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic
functions ${\mathcal H}(S)$. A companion survey provides equivalent definitions
and basic properties of these spaces as well as applications to function theory
and operator theory. The present survey brings to the fore more recent
applications to a variety of more elaborate function theory problems, including
$H^\infty$-norm constrained interpolation, connections with the Potapov method
of Fundamental Matrix Inequalities, parametrization for the set of all
solutions of an interpolation problem, variants of the Abstract Interpolation
Problem of Katsnelson, Kheifets, and Yuditskii, boundary behavior and boundary
interpolation in de Branges-Rovnyak spaces themselves, and extensions to
multivariable and Kre\u{\i}n-space settings.
