Diversity in time and space: wanted dead and alive

•We provide a framework for integrating paleontological and neontological research.•Our conceptual framework shows how fossil and contemporary data can be combined.•We give four examples of opportunities arising from a combined approach. Current patterns of biological diversity are influenced by both historical and present-day factors, yet research in ecology and evolution is largely split between paleontological and neontological studies. Responding to recent calls for integration, we provide a conceptual framework that capitalizes on data and methods from both disciplines to investigate fundamental processes. We highlight the opportunities arising from a combined approach with four examples: (i) which mechanisms generate spatial and temporal variation in diversity; (ii) how traits evolve; (iii) what determines the temporal dynamics of geographical ranges and ecological niches; and (iv) how species–environment and biotic interactions shape community structure. Our framework provides conceptual guidelines for combining paleontological and neontological perspectives to unravel the fundamental processes shaping life on Earth.