Yield gaps of major food crops are wide under rainfed family agriculture in the tropics. Their magnitude and causes vary substantially across agro-ecological, demographic and market situations. Methods to assess yield gaps should cope with spatio-temporal variability of bio-physical conditions, management practices, and data scarcity under smallholder conditions. Particularly challenging is to determine the most relevant methods for estimating potential (Yp) and water-limited (Yw) yields against which actual yields (Ya) are compared. We assessed yield gaps of main staple rainfed crops across contrasting family farming systems in Senegal (millet, subsistence oriented systems), central Brazil (maize, market oriented systems) and Vietnam (maize, market oriented systems and upland rice, subsistence oriented systems). In each region, actual aboveground biomass, Ya and yield components were measured over 2-3 agricultural seasons in a network of farmers' fields, covering the diversity of soils and farmers' management practices. Yp and Yw were calculated using a simple ad hoc crop simulation model (potential yield estimator, PYE) that was calibrated for each situation with observed and secondary data. Maize yields measured on farmers' fields were on average relatively high in market oriented systems, but extremely variable (4.14 ± 1.72 Mg ha?1). In contrast yields of crops of subsistence oriented systems were very low (0.80 ± 0.54 Mg ha?1 and 0.80 ± 0.47 Mg ha?1 for millet and upland rice, respectively). Ya ? Yp was 0.15 for millet in Senegal, 0.33 for upland rice in Vietnam, 0.26 for maize in Vietnam, and 0.46 for maize in Brazil. In Vietnam, there was little difference between Yw and Yp suggesting a low incidence of water constraints. The gap between Ya and Yw was equal to (millet in Senegal) or twice (maize in Vietnam and Brazil) the difference between Yw and Yp, indicating that yield gaps depend strongly on factors other than global radiation, temperature, rainfall and soil water holding capacity. Previous studies in the case study areas showed that the main causes of yield gaps were poor soil fertility and weed infestation related to the inability of farmers to access chemical inputs. Simple methods to estimate Yw and Yp, such as the values at the 90th percentile of Ya, or a bilinear boundary function fitted between seasonal rainfall and the best farmers' yield both led to strongly underestimated yield gaps. Yw and Yp estimated with a crop simulation model appeared to be more accurate, even in situations of relative scarcity of field data to calibrate cultivar-specific model parameters. (Résumé d'auteur)