We discuss a conformally invariant boundary version of the case of equality of the Ahlfors-Nehari-Schwarz lemma. The extremal functions are finite Blaschke product or faithful infinite analogs of

finite Blaschke products which we call maximal Blaschke products.

This result contains as a special case a boundary version of the Schwarz-Pick lemma which in turns implies the well-known boundary Schwarz lemma of Burns and Krantz. Based on joint work with Filippo Bracci and Daniela Kraus.