  An intriguing new duality between planar MHV gluon amplitudes and light-like
Wilson loops in N=4 super Yang-Mills is investigated. We extend previous checks
of the duality by performing a two-loop calculation of the rectangular and
pentagonal Wilson loop. Furthermore, we derive an all-order broken conformal
Ward identity for the Wilson loops and analyse its consequences. Starting from
six points, the Ward identity allows for an arbitrary function of conformal
invariants to appear in the expression for the Wilson loop. We compute this
function at six points and two loops and discuss its implications for the
corresponding gluon amplitude. It is found that the duality disagrees with a
conjecture for the gluon amplitudes by Bern et al. A recent calculation by Bern
et al indeed shows that the latter conjecture breaks down at six gluons and at
two loops. By doing a numerical comparison with their results we find that the
duality between gluon amplitudes and Wilson loops is preserved. This review is
based on the author's PhD thesis and includes developments until May 2008.
