Interest in predicting wheat yield in terms of physiological, cultural and meteorological variables is more than a century old. Early attempts involved statistical analyses of relationships between yield and observational data on precipitation, temperature, radiation, etc., and scientific study of physiological and cultural influences such as dates of sowing or anthesis, farming procedures and soil treatments. More recently these have been augmented by large-scale mechanistic models of phenological development, such as AFRCWHEAT, CERES and SIRIUS, incorporating some simulation facilities. All approaches implicitly involve fitting models of some sort: statistical, mechanistic or (preferably) a hybrid of these forms. Levels of success on this important matter are highly variable. After reviewing the field, we consider the results of recent efforts to contrast and evaluate the (large-scale) mechanistic approaches, using spatial/temporal methods for interpolating the required climatological input variables. The work employs a substantial database of wheat yields assembled for this purpose. After assessing the validity of the large-scale mechanistic models (with some intriguing conclusions), we then consider some results from a current approach to parsimonious hybrid modelling, based on statistical study of accessible climatological data interpreted in terms of physiological knowledge of key influences on plant development.