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Livestock grazing has degraded many arid and semi-arid rangelands around the world, and the drier climate predicted by climate change scenarios may amplify these effects and even lead to catastrophic vegetation shifts. We assess the long-term effects (1900-2100) of grazing and rainfall on various aspects of vegetation structure including the grass-shrub balance, the maintenance of spatial vegetation patterns, and the decline or recovery of palatable grasses (e.g. Poa ligularis) on a cover and/or density basis. We used the eco-hydrological and individual-based simulation model DINVEG for this purpose, which describes the spatiotemporal dynamics of Patagonian grass-shrub steppes based on six decades of field research (1955-2018). Rainfall and grazing affected the simulated vegetation structure in different ways. Total plant cover was mostly influenced by rainfall, but the cover of palatable grasses was mostly influenced by stocking rate. Dry conditions and low stocking rates (122 mm/year and <0.2 sheep/ha) favoured grasses over shrubs, whereas shrub encroachment occurred only in the high rainfall scenario combined with high stocking rates (181 mm/year and >0.2 sheep/ha). High stocking rates and/or drier conditions caused only gradual shifts in spatial vegetation patterns, but maintained the observed positive association for grasses around shrubs. In contrast, shrub encroachment was associated with repulsion between grasses and shrubs and the formation of shrub clusters into a matrix of scattered less palatable grasses. Plant compositional changes occurred through grass species replacement (e.g. P. ligularis is replaced by Pappostipa humilis) and the associated hysteresis effect of palatable grass species: model simulations suggest that 2-3 decades of heavy and year-long continuous grazing can drive palatable grasses to close to extinction, whereas natural recovery of degraded steppes may take 100 years or longer. Synthesis and applications. Desertification and climate change challenge grazing management in semi-arid rangelands, especially in already degraded ecosystems. Management that alternates between years of grazing and resting was effective to maintain the cover of palatable grasses, but this allowed for only very slow recovery of degraded steppes. While drier climate and grazing may not change the overall spatial patterns of vegetation, our results are rather pessimistic regarding the short-term recovery of palatable grasses. This will require increasing complexity in ecosystem restoration efforts, combined with interventions such as sowing, watering, reseeding or major changes in land use.