  Evidence has recently emerged for a hidden symmetry of scattering amplitudes
in N=4 super Yang-Mills theory called dual conformal symmetry. At weak coupling
the presence of this symmetry has been observed through five loops, while at
strong coupling the symmetry has been shown to have a natural interpretation in
terms of a T-dualized AdS_5. In this paper we study dual conformally invariant
off-shell four-point Feynman diagrams. We classify all such diagrams through
four loops and evaluate 10 new off-shell integrals in terms of Mellin-Barnes
representations, also finding explicit expressions for their infrared
singularities.
