  We study the integrability properties of Wilson loops in the ${\cal N}=6$
three-dimensional Chern-Simons-matter (ABJM) theory. We begin with the
construction of an open spin chain that describes the anomalous dimensions of
operators inserted along the contour of a 1/2 BPS Wilson loop. Moreover, we
compute the all-loop reflection matrices that govern the interaction of
spin-chain excitations with the boundary, including their dressing factors, and
we check them against weak- and strong-coupling results. Furthermore, we
propose a $Y$-system of equations for the cusped Wilson line of ABJM, and we
use it to reproduce the one-loop cusp anomalous dimension of ABJM from a
leading-order finite-size correction. Finally, we write a set of BTBA equations
consistent with the $Y$-system proposal.
