Superstrings in AdS in light cone gauge

We discuss light-cone gauge description of type IIB Green-Schwarz superstring in AdS_5 x S^5 with a hope to make progress towards understanding spectrum of this theory. As in flat space, fixing light cone gauge consists of two steps: (i) fixing kappa symmetry in such a way that the fermionic part of the action does not depend on x^-; (ii) fixing 2-d reparametrizations by x^+ = tau and a condition on 2-d metric. In curved AdS space the latter cannot be the standard conformal gauge and breaks manifest 2-d Lorentz invariance. It is natural, therefore, to work in phase-space framework, imposing the GGRT gauge conditions x^+= tau, P^+ =const. We obtain the resulting light cone superstring Hamiltonian. This is a review of hep-th/0007036 and hep-th/0009171.