  Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points
$z_1,z_2,\ldots, z_n\in \Omega$ and $w_1,w_2,\ldots, w_n\in \mathbb{D}$ (the
open unit disc in the complex plane), the \textit{Pick interpolation problem}
asks when there is a holomorphic function $f:\Omega \rightarrow
\overline{\mathbb{D}}$ such that $f(z_i)=w_i,1\leq i\leq n$. Pick gave a
condition on the data $\{z_i, w_i:1\leq i\leq n\}$ for such an $interpolant$ to
exist if $\Omega=\mathbb{D}$. Nevanlinna characterized all possible functions
$f$ that \textit{interpolate} the data. We generalize Nevanlinna's result to a
domain $\Omega$ in $\mathbb{C}^m$ admitting holomorphic test functions when the
function $f$ comes from the Schur-Agler class and is affiliated with a certain
completely positive kernel. The Schur class is a naturally associated Banach
algebra of functions with a domain. The success of the theory lies in
characterizing the Schur class interpolating functions for three domains - the
bidisc, the symmetrized bidisc and the annulus - which are affiliated to given
kernels.
