  This thesis is concerned with the study of scattering amplitudes in
four-dimensional conformal field theories, more particularly the N=4
super-Yang-Mills theory. We study this theory first at tree level by using
twistor space techniques and review the twistor string models that were
proposed to describe it. Then, we turn to the issue of iteration relations and
all loop ansatze for scattering amplitudes. We review the unitarity method for
computing scattering amplitudes and discuss the Wilson loop--scattering
amplitude duality that was inspired by the strong-coupling prescription of
Alday and Maldacena for scattering amplitudes. We describe in some detail the
computation of a two-loop six-point scattering amplitude and its surprising
equality to the polygonal Wilson loop.
