We study deep inelastic scattering in gauge theories which have dual string descriptions. As a function of gN we find a transition. For small gN, the dominant operators in the OPE are the usual ones, of approximate twist two, corresponding to scattering from weakly interacting partons. For large gN, double-trace operators dominate, corresponding to scattering from entire hadrons (either the original `valence' hadron or part of a hadron cloud.) At large gN we calculate the structure functions. As a function of Bjorken x there are three regimes: x of order one, where the scattering produces only supergravity states; x small, where excited strings are produced; and, x exponentially small, where the excited strings are comparable in size to the AdS space. The last regime requires in principle a full string calculation in curved spacetime, but the effect of string growth can be simply obtained from the world-sheet renormalization group.