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Context: Collection and analysis of large volumes of on-farm production data are widely seen as key to understanding yield variability among farmers and improving resource-use efficiency., Objective: The aim of this study was to assess the performance of statistical and machine learning methods to explain and predict crop yield across thousands of farmers' fields in contrasting farming systems worldwide., Methods: A large database of 10,940 field-year combinations from three countries in different stages of agricultural intensification was analyzed. Random effects models were used to partition crop yield variability and random forest models were used to explain and predict crop yield within a cross-validation scheme with data re-sampling over space and time., Results: Yield variability in relative terms was smallest for wheat and barley in the Netherlands and for wheat in Ethiopia, intermediate for rice in the Philippines, and greatest for maize in Ethiopia. Random forest models comprising a total of 87 variables explained a maximum of 65 % of cereal yield variability in the Netherlands and less than 45 % of cereal yield variability in Ethiopia and in the Philippines. Crop management related variables were important to explain and predict cereal yields in Ethiopia, while predictive (i.e., known before the growing season) climatic variables and explanatory (i.e., known during or after the growing season) climatic variables were most important to explain and predict cereal yield variability in the Philippines and in the Netherlands, respectively. Finally, model cross-validation for regions or years not seen during model training reduced the R 2 considerably for most crop x country combinations, while for wheat in the Netherlands this was model dependent., Conclusion: Big data from farmers' fields is useful to explain on-farm yield variability to some extent, but not to predict it across time and space., Significance: The results call for moderate expectations towards big data and machine learning in agronomic studies, particularly for smallholder farms in the tropics where model performance was poorest independently of the variables considered and the cross-validation scheme used., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors.)