Macroecology and biogeography are concerned with understanding biodiversity patterns across space and time. In the past, the two disciplines have addressed this question mainly with correlative approaches, despite frequent calls for more mechanistic explanations. Recent advances in computational power, theoretical understanding, and statistical tools are, however, currently facilitating the development of more system-oriented, mechanistic models. We review these models, identify different model types and theoretical frameworks, compare their processes and properties, and summarize emergent findings. We show that ecological (physiology, demographics, dispersal, biotic interactions) and evolutionary processes, as well as environmental and human-induced drivers, are increasingly modelled mechanistically; and that new insights into biodiversity dynamics emerge from these models. Yet, substantial challenges still lie ahead for this young research field. Among these, we identify scaling, calibration, validation, and balancing complexity as pressing issues. Moreover, particular process combinations are still understudied, and so far models tend to be developed for specific applications. Future work should aim at developing more flexible and modular models that not only allow different ecological theories to be expressed and contrasted, but which are also built for tight integration with all macroecological data sources. Moving the field towards such a 'systems macroecology' will test and improve our understanding of the causal pathways through which eco-evolutionary processes create diversity patterns across spatial and temporal scales.