  I describe some recent developments in the understanding of gluon scattering
amplitudes in N=4 super-Yang-Mills theory in the large-N_c limit. These
amplitudes can be computed to high orders in the weak coupling expansion, and
also now at strong coupling using the AdS/CFT correspondence. They hold the
promise of being solvable to all orders in the gauge coupling, with the help of
techniques based on integrability. They are intimately related to expectation
values for polygonal Wilson loops composed of light-like segments.
