Understanding the structure and functioning of river ecosystems is an overarching objective of ecology. Numerous models have been developed to expand our knowledge of the functioning of riverine ecosystems, but most are ‘best approximations’ of existing knowledge. Here, we present the ‘Savanna River Ecosystem Model (SREM)' for rivers draining savanna and grassland ecosystems that have traditionally supported high numbers of large mammalian herbivores (LMH). LMH significantly modify the structure and function of river ecosystems in these landscapes through hoof action and transfer of nutrients and organic matter from terrestrial to the aquatic domain through excretion and egestion during watering or resting and accidental death during migrations. This lateral connectivity between savanna rivers and their terrestrial milieu occurs at times and locations in the river network when and for which allochthonous inputs are traditionally rarely conceptualized. Thus, at a large spatial scale, savanna rivers may function differently compared to predictions by most existing models. Drawing from literature and data on savanna rivers where wild LMH populations are still dominant, we present a conceptual model that recognizes the role of LMH as major drivers of ecosystem structure and function. The influence of LMH is dependent upon the characteristics of the LMH (e.g., species, number of individuals, behaviour), which interact with the characteristics of rivers (e.g., stream size, flow regime) to drive ecosystem processes such as metabolism, nutrient processing and outgassing of greenhouse gases. We explore the implications of our findings for the understanding and managing rivers in increasingly altered landscapes, where large populations of wild LMH have either been lost or displaced by livestock. Finally, we make recommendations for future research and propose actions needed to preserve savanna rivers.