Increasing food demand under climate change constraints may challenge and strain agricultural systems. The use of crop models to assess genotypes performance across diverse target environments and management practices, i.e., the genetic × environment × management interaction (GEMI), can help understand suitability of genotype and agronomic practices, and possibly accelerate turnaround in plant breeding programs. However, the readiness of models to support these tasks can be debated. In this article, we point out modeling and data limitations and argue the need for evaluation and improvement of relevant process algorithms as well as model convergence. Under conditions suitable for plant growth, without meteorological extremes or soil limitation to root exploration, models can simulate resource capture, growth, and yield with relative ease. As stresses accumulate, the plant species-and genotype-specific attributes and their interactions with the soil and atmospheric environment generate a large range of responses, including conditions where resources become so limiting as to make yields very low. The space in between high and low yields is where most rainfed production occurs, and where the current model and user skill at representing GEMI varies. We also review studies comparing the performance of a large number of crop models and the lessons learned. The overall message is that improvement of models appears as a necessary condition for progress, and perhaps relevancy. Model ensembles help mitigate data input, model, and user-driven uncertainty for some but not all applications, sometimes at a very high cost. Successful model-based assessment of GEMI not only requires better crop models and knowledgeable users, but also a realistic representation of the environmental conditions of the landscape where crops are grown, which is not trivial given the 3D nature of water and nutrient transport. Models remain the best quantitative repository of our knowledge on crop functioning; they contain a narrative of plant, soil, and atmospheric functioning in computer language and train the mind to couple processes. But in our quest to tame GEMI, will they lead the way or just ride along history?