Historical increases in agricultural production were achieved predominantly by large increases in agricultural productivity. Intensification of crop and livestock production also plays a key role in future projections of agricultural land use. Here, we assess and discuss projections of crop yields by global agricultural land-use and integrated assessment models. To evaluate these crop yield projections, we compare them to empirical data on attainable yields by employing a linear and plateauing continuation of observed attainable yield trends. While keeping in mind the uncertainties of attainable yields projections and not considering future climate change impacts, we find that, on average for all cereals on the global level, global projected yields by 2050 remain below the attainable yields. This is also true for future pathways with high technological progress and mitigation efforts, indicating that projected yield increases are not overly optimistic, even under systemic transformations. On a regional scale, we find that for developing regions, specifically for sub-Saharan Africa, projected yields stay well below attainable yields, indicating that the large yield gaps which could be closed through improved crop management, may also persist in the future. In OECD countries, in contrast, current yields are already close to attainable yields, and the projections approach or, for some models, even exceed attainable yields by 2050. This observation parallels research suggesting that future progress in attainable yields in developed regions will mainly have to be achieved through new crop varieties or genetic improvements. The models included in this study vary widely in their implementation of yield progress, which are often split into endogenous (crop management) improvements and exogenous (technological) trends. More detail and transparency are needed in these important elements of global yields and land use projections, and this paper discusses possibilities of better aligning agronomic understanding of yield gaps and yield potentials with modelling approaches.