In this thesis we develop techniques of integrability in the study of dualities between two-dimensional conformal field theories and theories of closed strings on three-dimensional Anti-de Sitter background geometries. For several years after integrability was first applied to the 3d/2d dualities, it was an unanswered question how to incorporate the so-called \massless modes" of these theories into the integrability machinery. Here we tackle this problem in several contexts. We show that in the classical integrable description of closed strings the implementation of the string Virasoro constraints needs to be modified for geometries with multiple factors where massless modes are present. We show further that with the correct implementation of the Virasoro constraints, massless modes can be included in integrability techniques for obtaining quantum corrections to physical quantities such as the energies of string solutions. Lastly, we consider the scattering of fundamental string excitations and derive all-loop expressions for the scattering matrix that includes both massless and massive excitations.