  While many classes of cutting-planes are at the disposal of integer
programming solvers, our scientific understanding is far from complete with
regards to cutting-plane selection, i.e., the task of selecting a portfolio of
cutting-planes to be added to the LP relaxation at a given node of the
branch-and-bound tree. In this paper we review the different classes of
cutting-planes available, known theoretical results about their relative
strength, important issues pertaining to cut selection, and discuss some
possible new directions to be pursued in order to accomplish cutting-plane
selection in a more principled manner. Finally, we review some lines of work
that we undertook to provide a preliminary theoretical underpinning for some of
the issues related to cut selection.
