A hinge for mounting a door on a piece of furniture or the like comprises a hinge arm, a box connected to the hinge arm by an articulation system comprising a plurality of movable connecting levers and seven articulation axes, spring means acting in closing direction of the hinge, and a damping device having an actuation member linearly movable according to a longitudinal axis; the damping device is at least partially enclosed between the side walls of the hinge arm, and the actuation member of the damping device extends at a front end of the hinge arm facing the hinge box for contacting thrust element of one of the connecting levers of the articulation system or integral with one of the connecting levers or with the hinge box at least in a range near the closing position of the hinge.