  Recent progress towards understanding a strong coupling expansion for various
superconformal field theories in four dimensions is described. First, the case
of the maximally supersymmetric Yang Mills theory is analyzed, as well as many
calculations that can be done directly at strong coupling and matched to the
AdS dual geometry. Also, this understanding is extended to other AdS duals
where the sphere is replaced by a Sasaki-Einstein manifold. Particular emphasis
is made on matching exactly part of the supergravity dual spectrum of various
of these field theories by using wave function methods.
