Scattering amplitudes in N=4 super-Yang-Mills theory can be defined in dimensional regularization near four dimensions, and have a number of remarkable features. There is good evidence for an exact, all-loop formula for the planar four- and five-point scattering amplitudes in terms of four functions of the coupling alone, one of which is the cusp anomalous dimension. For six gluons this particular formula fails. However, for the 'MHV' helicity configuration, an equivalence to a Wilson line expectation value on a hexagon persists at two loops, as does a certain 'dual conformal invariance'. These properties are connected to features of string propagation in AdS(5) x S5, in particular T duality.