Abstract: Based on equilibrium theoretical models, the response of vegetation to grazing pressure is linear and reversible, and can be manipulated predictably with stocking rates. This equilibrium-based theoretical model advocates a conservative stocking strategy to maintain internal ecosystem regulation and stability. The management goal is to maintain a balance between stocking numbers and feeding resources. In contrast, 'new rangeland science' based on non-equilibrium ecological dynamics placed greater emphasis on external disturbances as drivers of ecosystem behavior. The ‘new science’, proposes that plant composition and biomass in semi-arid rangelands are primarily driven by rainfall and not by grazing pressure. Management of such systems should be opportunistic and take advantage of, or create, conditions which allow switches to a more desirable state. There are two major approaches: plant- or animal-oriented, to determine rangeland carrying capacity (CC). The traditional technique for determining CC is to calculate the total amount of forage at the end of the growing season, multiply this by a correction factor, and then divide by the average yearly feeding requirements of a livestock unit. Using total herbaceous forage productivity as the single criterion to predict the livestock support capacity has been criticized because biomass quality and feeding value for livestock and livestock nutritional needs are largely ignored. Based on research progress, the development and evolution, controversy in the application of the CC concept are summarized. The plant-, animal- (including standard hay-, total digestible nutrients- digestible crude protein- and energy-oriented) oriented CC was also compared. It is evident that in view of the seasonal variation in nutrient content of natural herbage, animal-oriented permissible stocking rates on the whole tend to be lower than those predicted by the plant-oriented approach. The most complete approach to evaluate primary and secondary productivity of rangelands should combine plant- and animal-based methods, rather than just plant oriented. In the case of a conservative grazing strategy, stocking rate was stable and grazing pressure fluctuated while for an opportunistic grazing strategy, stocking rate was unstable and grazing pressure was stable. Both equilibrium and non-equilibrium dynamics are found in rangelands, often at different times or governing different parts of the resource. Either conservative or opportunistic strategies could be correct, depending on the circumstances, including environmental variability and predictability, degradation and thresholds, property right regimes, discount rates, and market stability and prices. Finally, rangeland science and management are ultimately based on ecological models. In making management decisions, the specific model used is important because it determines both the expected ecosystem response to particular actions, as well as the strategies to attain desired conditions. The ecological model and grazing lands applications are summed up to provide reference for grazing management decision.