This final Chapter applies and develop discrete weak KAM theoryweak KAMtheory in the context conservative twist mapstwist maps of the annulus. This is the original setting in which Aubry–Mather theory wasAubry-Mather theory conceived and strangely, weak KAM solutions were not very much studied in this setting until quite recently. In this Chapter we present the very special features of Aubry and Mather setsMatherset in this low dimensional setting. We then study and characterize weak KAM solutions for those twist maps, we describe the shape of their derivative. Finally (partially without proof) we present results related to, more or less weak, integrability properties of twist maps.