Argyres-Douglas (AD) theories are 4d N=2
superconformal field theories without useful Lagrangian
descriptions. Therefore their superconformal indices
cannot be evaluated by supersymmetric localization. In
this talk, I will discuss our conjectural expression for the
superconformal index of AD theories given in terms of 2d
q-deformed Yang-Mills theory. Our conjecture is based
on the S^1 x S^3 version of the AGT relation, and is
perfectly consistent with the Higgs branch chiral rings, 2d
chiral algebras, RG-flows, and the 3d reduction of AD
theories.