Crop models are essential tools in climate change impact assessments, but they often lack comprehensive field testing. In this study, we tested the SUBSTOR-potato model with 87 field experiments, including 204 treatments from 19 countries. The field experiments varied in potato species and cultivars, N fertilizer application, water supply, sowing dates, soil types, temperature environments, and atmospheric CO2 concentrations, and included open top chamber and Free-Air-CO2-Enrichment (FACE) experiments. Tuber yields were generally well simulated with the SUBSTOR-potato model across a wide range of current growing conditions and for diverse potato species and cultivars, including Solanum tuberosum, Solanum andigenum, Solanum juzepczukii species, as well as modern, traditional, early, medium, and late maturity-type cultivars, with a relative RMSE of 37.2% for tuber dry weight and 21.4% for tuber fresh weight. Cultivars ‘Desiree’ and ‘Atlantic’ were grown in experiments across the globe and well simulated using consistent cultivar parameters. However, the model underestimated the impact of elevated atmospheric CO2 concentrations and poorly simulated high temperature effects on crop growth. Other simulated crop variables, including leaf area, stem weight, crop N, and soil water, differed frequently from measurements; some of these variables had significant large measurement errors. The SUBSTOR-potato model was shown to be suitable to simulate tuber growth and yields over a wide range of current growing conditions and crop management practices across many geographic regions. However, before the model can be used effectively in climate change impact assessments, it requires improved model routines to capture the impacts of elevated atmospheric CO2 and high temperatures on crop growth.