  Wilson loops are calculated within the AdS/CFT correspondence by finding a
classical solution to the string equations of motion in AdS_5 x S^5 and
evaluating its action. An important fact is that this sigma-model used to
evaluate the Wilson loops is integrable, a feature that has gained relevance
through the study of spinning strings carrying large quantum numbers and
spin-chains. We apply the same techniques used to solve the equations for
spinning strings to find the minimal surfaces describing a wide class of Wilson
loops. We focus on different cases with periodic boundary conditions on the
AdS_5 and S^5 factors and find a rich array of solutions. We examine the
different phases that appear in the problem and comment on the applicability of
integrability to the general problem.
