I will summarise recent developments which indicate that there is a surprising duality between gluon amplitudes and Wilson loops in supersymmetric Yang-Mills theory. The motivation for the duality comes from the proposal for the strong coupling form of gluon amplitudes due to Alday and Maldacena. The evidence that the duality holds also at weak coupling comes from direct calculations of both objects and an analysis of a surprising 'dual' conformal symmetry of the gluon amplitudes which has a natural interpretation for the Wilson loops.