In this talk we will discuss some problems about interpolation in Hilbert spaces of analytic functions and their multiplier algebras. In particular we give a positive answer to a question raised by J. E. McCarthy and J. Agler about strong separation and simply interpolating sequences in reproducing kernel Hilbert spaces with the complete Nevanlinna Pick property. Furthermore, we use a result of A. F. Beardon from Fuchsian groups to show that, in the same class of spaces, there exist sequences with infinite associated measure which are simply interpolating.