With ever-growing data availability and computational power at our disposal, we now have the capacity to use process-explicit models more widely to reveal the ecological and evolutionary mechanisms responsible for spatiotemporal patterns of biodiversity. Most research questions focused on the distribution of diversity cannot be answered experimentally, because many important environmental drivers and biological constraints operate at large spatiotemporal scales. However, we can encode proposed mechanisms into models, observe the patterns they produce in virtual environments, and validate these patterns against real-world data or theoretical expectations. This approach can advance understanding of generalizable mechanisms responsible for the distributions of organisms, communities, and ecosystems in space and time, advancing basic and applied science. We review recent developments in process-explicit models and how they have improved knowledge of the distribution and dynamics of life on Earth, enabling biodiversity to be better understood and managed through a deeper recognition of the processes that shape genetic, species, and ecosystem diversity.