Global vegetation and land-surface models embody interdisciplinary scientific understanding of the behaviour of plants and ecosystems, and are indispensable to project the impacts of environmental change on vegetation and the interactions between vegetation and climate. However, systematic errors and persistently large differences among carbon and water cycle projections by different models highlight the limitations of current process formulations. In this review, focusing on core plant functions in the terrestrial carbon and water cycles, we show how unifying hypotheses derived from eco-evolutionary optimality (EEO) principles can provide novel, parameter-sparse representations of plant and vegetation processes. We present case studies that demonstrate how EEO generates parsimonious representations of core, leaf-level processes that are individually testable and supported by evidence. EEO approaches to photosynthesis and primary production, dark respiration and stomatal behaviour are ripe for implementation in global models. EEO approaches to other important traits, including the leaf economics spectrum and applications of EEO at the community level are active research areas. Independently tested modules emerging from EEO studies could profitably be integrated into modelling frameworks that account for the multiple time scales on which plants and plant communities adjust to environmental change.