This paper seeks to survey, understand and reconcile the widely divergent estimates of long run global crop output, land use and price projections in the current literature. We begin by reviewing the history of such projections and the different models and assumptions used in these exercises. We then introduce an analytical partial equilibrium model of the global crops sector which provides a lens through which we can evaluate this previous work. The resulting decomposition of model responses into demand, extensive supply and intensive supply elasticities offers important insights into the diversity of model parameterizations being employed by the existing models. This, along with the methodology for implementing productivity growth, helps explain some of the divergences in results. We conclude the review by employing a numerical version of the analytical model, which serves as an emulator of this entire class of models, in order to explore how uncertainties in the common underlying drivers and economic responses contribute to uncertain projections of output, prices and land use in 2050. We place each of the published estimates reviewed within this paper into the resulting empirical distribution of outcomes at mid-century. In addition, we quantify the sensitivity of these projections to model inputs. Our findings suggest that the top priority for future research should be improved estimation of agricultural factor supply elasticities – a topic which has been largely neglected in recent decades.