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Human water use has significantly increased during the recent past. Water withdrawals from surface and groundwater sources have altered terrestrial discharge and storage, with large variability in time and space. These withdrawals are driven by sectoral demands for water, but are commonly subject to supply constraints, which determine water allocation. Water supply and allocation, therefore, should be considered together with water demand and appropriately included in Earth system models to address various large-scale effects with or without considering possible climate interactions. In a companion paper, we review the modeling of demand in large-scale models. Here, we review the algorithms developed to represent the elements of water supply and allocation in land surface and global hydrologic models. We note that some potentially important online implications, such as the effects of large reservoirs on land–atmospheric feedbacks, have not yet been fully investigated. Regarding offline implications, we find that there are important elements, such as groundwater availability and withdrawals, and the representation of large reservoirs, which should be improved. We identify major sources of uncertainty in current simulations due to limitations in data support, water allocation algorithms, host large-scale models as well as propagation of various biases across the integrated modeling system. Considering these findings with those highlighted in our companion paper, we note that advancements in computation and coupling techniques as well as improvements in natural and anthropogenic process representation and parameterization in …