Abstract Global bioenergy potentials have been the subject of extensive research and continued controversy. Due to vast uncertainties regarding future yields, diets and other influencing parameters, estimates of future agricultural biomass potentials vary widely. Most scenarios compatible with ambitious climate targets foresee a large expansion of bioenergy, mainly from energy crops that needs to be kept consistent with projections of agriculture and food production. Using the global biomass balance model BioBaM, we here present an assessment of agricultural bioenergy potentials compatible with the Food and Agriculture Organization’s (2018) ‘Alternative pathways to 2050’ projections. Mobilizing biomass at larger scales may be associated with systemic feedbacks causing greenhouse gas (GHG) emissions, e.g. crop residue removal resulting in loss of soil carbon stocks and increased emissions from fertilization. To assess these effects, we derive ‘GHG cost supply-curves’, i.e. integrated representations of biomass potentials and their systemic GHG costs. Livestock manure is most favourable in terms of GHG costs, as anaerobic digestion yields reductions of GHG emissions from manure management. Global potentials from intensive livestock systems are about 5 EJ/yr. Crop residues can provide up to 20 EJ/yr at moderate GHG costs. For energy crops, we find that the medium range of literature estimates (∼40 to 90 EJ/yr) is only compatible with FAO yield and human diet projections if energy plantations expand into grazing areas (∼4–5 million km2) and grazing land is intensified globally. Direct carbon stock changes associated with perennial energy crops are beneficial for climate mitigation, yet there are—sometimes considerable—‘opportunity GHG costs’ if one accounts the foregone opportunity of afforestation. Our results indicate that the large potentials of energy crops foreseen in many energy scenarios are not freely and unconditionally available. Disregarding systemic effects in agriculture can result in misjudgement of GHG saving potentials and flawed climate mitigation strategies.