Bioenergy is projected to have a prominent, valuable, and maybe essential, role in climate management. However, there is significant variation in projected bioenergy deployment results, as well as concerns about the potential environmental and social implications of supplying biomass. Bioenergy deployment projections are market equilibrium solutions from integrated modeling, yet little is known about the underlying modeling of the supply of biomass as a feedstock for energy use in these modeling frameworks. We undertake a novel diagnostic analysis with ten global models to elucidate, compare, and assess how biomass is supplied within the models used to inform long-run climate management. With experiments that isolate and reveal biomass supply modeling behavior and characteristics (costs, emissions, land use, market effects), we learn about biomass supply tendencies and differences. The insights provide a new level of modeling transparency and understanding of estimated global biomass supplies that informs evaluation of the potential for bioenergy in managing the climate and interpretation of integrated modeling. For each model, we characterize the potential distributions of global biomass supply across regions and feedstock types for increasing levels of quantity supplied, as well as some of the potential societal externalities of supplying biomass. We also evaluate the biomass supply implications of managing these externalities. Finally, we interpret biomass market results from integrated modeling in terms of our new understanding of biomass supply. Overall, we find little consensus between models on where biomass could be cost-effectively produced and the implications. We also reveal model specific biomass supply narratives, with results providing new insights into integrated modeling bioenergy outcomes and differences. The analysis finds that many integrated models are considering and managing emissions and land use externalities of supplying biomass and estimating that environmental and societal trade-offs in the form of land emissions, land conversion, and higher agricultural prices are cost-effective, and to some degree a reality of using biomass, to address climate change.