Ever more stringent emissions and fuel consumption legislations require OEMs to introduce engine measures which reduce emissions and improve the operating conditions of the After Treatment System (ATS) at all engine operating points. The heavy-duty engine, for diesel or alternative fuels, runs extensively also in negative torque operating modes, particularly for on-road applications. In this paper we review the fuel cut-off engine operation, and how various measures introduced for operation in positive torque modes can be optimized for engine performance in negative torque regime. During engine motoring, performance criteria may include low motoring torque, reduced cooling of the ATS as well as priming of the turbine for the case of an eventual load request. We review and analyze, based on experimental data from a typical HD on-road engine, the impact of various measures, including Cylinder Deactivation (with various combinations of deactive cylinders), Miller camshafts, intake and exhaust throttling, and Exhaust Gas Recirculation. We will then extend the focus of negative torque to the need for engine braking, and we review the braking performance capability comparing the utilization of throttling in standard four-stroke operation, and the improvements obtained for high-power engine brake with the introduction of decompression humps in the valve lift profile. We introduce a quasi two-stroke brake system, which can reach very high braking power without requiring changes to the standard intake valve lift as pure two-stroke brake would. It completes each breathing, compression and decompression cycle in every consecutive two engine strokes, but whereas the first of each pair of cycles breathes and brakes with fresh air, the second re-breathes, compresses and decompresses brake gas.