Most studies of cross-ecosystem resource subsidies have demonstrated positive effects on recipient consumer populations, often with very large effect sizes. However, it is important to move beyond these initial addition–exclusion experiments to consider the quantitative consequences for populations across gradients in the rates and quality of resource inputs. In our introduction to this special issue, we describe at least four potential models that describe functional relationships between subsidy input rates and consumer responses, most of them asymptotic. Here we aim to advance our quantitative understanding of how subsidy inputs influence recipient consumers and their communities. In the papers following, fish were either the recipient consumers or the subsidy as carcasses of anadromous species. Advancing general, predictive models will enable us to further consider what other factors are potentially co-limiting (e.g., nutrients, other population interactions, physical habitat, etc.) and better integrate resource subsidies into consumer–resource, biophysical dynamics models.