Potassium (K) is essential for a wide range of physiological functions in plants, and a limiting element for wood productivity in numerous forest ecosystems. However, the contribution of each of the K-sensitive physiological processes to the limitation of wood productivity is poorly known. In trees, K deficiency acts both on the source and the sinks of carbon making it difficult to disentangle its effects on wood productivity. Here, we review the literature dealing with the influence of K-limitation on tree physiological processes. Results from extensively studied tropical Eucalyptus plantations are used to illustrate the physiological processes the most impacted by K deficiency. We identify the main processes that limit the availability of K to the trees and influence the circulation of K ions in the ecosystem. Then, we describe the influence of K bioavailability on carbon assimilation, the water economy of trees, and carbon partitioning. We conclude this review by identifying the main priorities towards the process-based modelling of the influence of K on the carbon and water cycles in forest ecosystems. For each process modelling priority, we identify options that could be used in the current conceptual framework of most eco-physiological models.