Vegetation plays an essential role in regulating carbon and water cycles, e.g. by taking up atmospheric CO₂ through photosynthesis and by transferring soil water to the atmosphere through transpiration. Vegetation function is shaped by its structure and physiology: vegetation structure is determined by the amount of materials for plants and how it is organised in space and time, while vegetation physiology controls the instantaneous response of vegetation function to environmental conditions. Recognizing and disentangling these aspects of vegetation is key to understanding and predicting the response of the terrestrial biosphere to global change. This is now possible, as comprehensive measurements from Earth observations, both from satellites and the ground, provide invaluable data and information. This review introduces and describes vegetation structure and physiology, and summarises, compares, and contextualises recent literature to illustrate the state of the art in monitoring vegetation dynamics, quantifying large-scale vegetation physiology, and investigating vegetation regulation on the changes of global carbon and water fluxes. This includes results from remote sensing, in-situ measurements, and model simulations, used either to study the response of vegetation structure and physiology to global change, or to study the feedback of vegetation to global carbon and water cycles. We find that observation-based work is underrepresented compared with model-based studies. We therefore advocate further work to make better use of remote sensing and in-situ measurements, as they promote the understanding of vegetation dynamics from a fundamental data-driven perspective. We highlight the usefulness of novel and increasing satellite remote sensing data to comprehensively investigate the structural and physiological dynamics of vegetation on the global scale, and to infer their influence on the land carbon sink and terrestrial evaporation. We argue that field campaigns can and should complement large-scale analyses together with fine spatio-temporal resolution satellite remote sensing to infer relevant ecosystem-scale processes.