We shall present a characterization of simply interpolating sequences in the Dirichlet space. The same characterization is conjectured to hold in all complete Nevanlinna Pick spaces but the problem remains open despite recent progress. Finally, we are going to discuss some variants of the classical interpolation problem, such as random interpolation. This is a field where numerous questions remain open. Extended abstract: https://site.unibo.it/complex-analysis-lab/en/news-1/piniseminarabstract.pdf/@@download/file/PiniSeminarAbstract.pdf