In this paper we study the spectrum of BPS operators/states in N = 2 super- conformal U(N) Chern-Simons-matter theories with adjoint chiral matter fields, with and without superpotential. The superconformal indices and conjectures on the full supersym- metric spectrum of the theories in the large N limit with up to two adjoint matter fields are presented. Our results suggest that some of these theories may have supergravity duals at strong coupling, while some others may be dual to higher spin theories of gravity at strong coupling. For the N = 2 theory with no superpotential, we study the renormalization of R-charge at finite 't Hooft coupling using "Z-minimization". A particularly intriguing result is found in the case of one adjoint matter. © 2012 SISSA.