  We perform a detailed study of the Yangian symmetry of smooth supersymmetric
Maldacena-Wilson loops in planar N=4 super Yang-Mills theory. This hidden
symmetry extends the global superconformal symmetry present for these
observables. A gauge-covariant action of the Yangian generators on the Wilson
line is established that generalizes previous constructions built upon path
variations. Employing these generators the Yangian symmetry is proven for
general paths in non-chiral N=4 superspace at the first perturbative order. The
bi-local piece of the level-one generators requires the use of a regulator due
to divergences in the coincidence limit. We perform regularization by point
splitting in detail, thereby constructing additional local and boundary
contributions as regularization for all level-one Yangian generators. Moreover,
the Yangian algebra at level one is checked and compatibility with local
kappa-symmetry is established. Finally, the consistency of the Yangian symmetry
is shown to depend on two properties: The vanishing of the dual Coxeter number
of the underlying superconformal algebra and the existence of a novel
superspace "G-identity" for the gauge field theory. This tightly constrains the
conformal gauge theories to which integrability can possibly apply.
