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Summary In savannas, degrading trends such as increasing woody cover are caused by livestock ranging. Hence, identifying sustainable utilisation intensities is crucial for range management. However, knowledge concerning herbivory effects on herbaceous vegetation and primary productivity, but also productivity of and foraging on woody vegetation (browsing) is incomplete. Consequences of these knowledge gaps for predictions of long-term herbivory impacts are analysed by exploring a set of herbivory models in the framework of a spatially explicit simulator of vegetation dynamics in a semiarid savanna. We distinguish herbaceous and woody vegetation, and two impacts of herbivory, namely on phytomass and on primary productivity. Herbaceous phytomass is consumed under all grazing models, which are distinct by effects on herbaceous productivity per unit ground area: none; direct effect on productivity; direct effects on productivity and survival. Browsing is either absent or present. Additionally, low and high spatial grazing heterogeneity are distinguished. For a time scale of 100 years, herbivory impacts were analysed in a simulation experiment over a range of low to high stocking rates. Without effects on primary productivity, herbivory showed no long-term impact on shrub cover. However, under higher stocking rates, mean herbage utilisation reached over 50% of herbaceous phytomass production, rendering the null hypothesis on productivity effects of herbivory unrealistic. When grass productivity was affected by herbivory, shrub cover showed a threshold response to utilisation intensity: at low subcritical intensities, shrub cover did not exceed the low initial values; above a threshold intensity, savanna vegetation was characterised by high shrub cover. The level of this threshold was affected by heterogeneity, browsing, and by the nature of the productivity effects, and also depended on the time span considered. Since sustainable livestock ranging is possible only at utilisation intensities below this threshold, its determinants are crucial for long-term assessments. Given the insufficient quantitative understanding of all three of the factors determining long-term herbivory impacts, our results suggest caution towards current predictions, and provide for a priority ranking in urgently needed further research.