A sequence $(z_n)$ in the unit disc is called an interpolating sequence for $H^\infty$ if for every bounded sequence of values $(w_n)$, there exists a bounded analytic function $f$ in the disc such that $f(z_n) = w_n$ for all $n$. Such sequences were characterized by Lennart Carleson. I will talk about a generalization of Carleson's theorem to other classes of functions. The proof of this result uses the solution of the Kadison-Singer problem due to Marcus, Spielman and Srivastava. This is joint work with Alexandru Aleman, John McCarthy and Stefan Richter.