A well known result of Giroux tells us that isotopy classes
of contact structures on a closed three manifold are in one to one
correspondence with stabilization classes of open book decompositions
of the manifold. We will introduce a stabilization-invariant property
of open books which corresponds to tightness of the corresponding
contact structure. We will mention applications to the classification
of contact 3-folds, and also to the question of whether tightness is
preserved under Legendrian surgery.