The economic effects of climate change on agriculture have been widely assessed in the last two decades. Many of these assessments are based on the integration of biophysical and agro-economic models, allowing to understand the physical and socio-economic responses of the agricultural sector to future climate change scenarios. The evolution of the bio-economic approach has gone through different stages. This review analyses its evolution: firstly, framing the bio-economic approach into the context of the assessments of climate change impacts, and secondly, by reviewing empirical studies at the global and European level. Based on this review, common findings emerge in both global and regional assessments. Among them, the authors show that overall results tend to hide significant disparities on smaller spatial scales. Furthermore, due to the effects of crop prices over yield changes, several authors highlight the need to consider endogenous price models to assess production impacts of climate change. Further, major developments are discussed: the progress made since the last two decades and the recent methods used to provide insights into modeling uncertainties. However, there are still challenges to be met. On this matter, the authors take these unresolved challenges as guidelines for future research.