There has been much recent interest in the proposed duality between superstrings in the curved geometry AdS_4 x P3 and three dimensional N=6 supersymmetric Chern-Simons theory -- a new, concrete, example of the holographic AdS/CFT correspondence. This dual pair has additionally been conjectured to be an integrable system in the planar limit. In this talk I will discuss several classes of classical strings moving in this background, and their quantum corrections, as tools to probe the duality and to test the conjectured integrable structure.