Animal-source foods are a major component of global diets and are increasingly criticised because of their adverse impacts on environment, climate and health. A shift in diets towards plant-based foods is a discussed option to overcome these problems. Much of the scientific emphasis so far has been on estimating the potential of such a dietary change to reduce greenhouse gas emissions and improve health outcomes while less attention has been attracted on studies analysing the impacts on agricultural markets. This paper aims to provide a comprehensive overview and, therefore, summarizes existing studies on the effects of a reduced consumption of animal-source foods on agricultural markets, greenhouse gas emissions, food security and health. In addition, available studies on the so‑called rebound effect are presented. The identified studies suggest that a reduction in the consumption of meat in the EU or OECD would lead to a 1‑10% decrease in meat world market prices, depending on the magnitude and particularities of the assumed dietary changes. This would translate to a 3‑10% reduction in production. The lower domestic demand for meat could also negatively affect welfare outcomes and GDP. However, it has to be mentioned that these studies do not take into account the consequences of improved environmental and health conditions. In fact, our review indicates that reductions in greenhouse gas emissions could generally be proportional to the magnitude of plant-based diets. The maximum reduction potentials of 60-70% could be found for global vegetarian or vegan diets. However, some studies indicate that a shift in food expenditure towards other resource-intensive goods could lead to a rebound effect. Further, this overview suggests that environmental and public health objectives might be in alignment as all identified studies indicate that a reduction in meat consumption in high‑income countries could be associated with lower rates of mortality and non-communicable diseases. This overview reveals the complex relationships between food demand, agricultural supply, international trade, environment, health and food security.