Any four dimensional N=2 superconformal field theory (SCFT) contains a subsector of local operator which is isomorphic to a two dimensional chiral algebra. If the 4d theory possesses N=3 or N= 4 superconformal symmetry, the corresponding chiral algebra is an extension the N=2 or (small) N=4 super-Virasoro algebra respectively. In this talk I will present some results on the classification of N=4 chiral algebras and discuss if they can correspond to a 4d theory.