Abstract. This review focuses on recent advances in some key areas of wheat physiology, namely phasic development, determination of potential yield and water-limited potential yield, tolerance to some other abiotic stresses (aluminium, salt, heat shock), and simulation modelling. Applications of the new knowledge to breeding and crop agronomy are emphasized. The linking of relatively simple traits like time to flowering, and aluminium and salt tolerance, in each case to a small number of genes, is being greatly facilitated by the development of molecular gene markers, and there is some progress on the functional basis of these links, and likely application in breeding. However with more complex crop features like potential yield, progress at the gene level is negligible, and even that at the level of the physiology of seemingly important component traits (e.g., grain number, grain weight, soil water extraction, sensitivity to water shortage at meiosis) is patchy and generally slow although a few more heritable traits (e.g. carbon isotope discrimination, coleoptile length) are seeing application. This is despite the advent of smart tools for molecular analysis and for phenotyping, and the move to study genetic variation in soundly-constituted populations. Exploring the functional genomics of traits has a poor record of application; while trait validation in breeding appears underinvested. Simulation modeling is helping to unravel G Â E interaction for yield, and is beginning to explore genetic variation in traits in this context, but adequate validation is often lacking. Simulation modelling to project agronomic options over time is, however, more successful, and has become an essential tool, probably because less uncertainty surrounds the influence of variable water and climate on the performance of a given cultivar. It is the everincreasing complexity we are seeing with genetic variation which remains the greatest challenge for modelling, molecular biology, and indeed physiology, as they all seek to progress yield at a rate greater than empirical breeding is achieving.