The last 20 years since the previous World Congress have seen tremendous advancements in quantitative genetics, in large part due to the advancements in genomics, computation, and statistics. One central theme of this last 20 years has been the exploitation of the vast harvest of molecular markers—examples include QTL and association mapping, marker-assisted selection and introgression, scans for loci under selection, and methods to infer degree of coancestry, population membership, and past demographic history. One consequence of this harvest is that phenotyping, rather than genotyping, is now the bottleneck in molecular quantitative genetics studies. Equally important have been advances in statistics, many developed to effectively use this treasure trove of markers. Computational improvements in statistics, and in particular Markov Chain Monte Carlo (MCMC) methods, have facilitated many of these methods, as have significantly improved computational abilities for mixed models. Indeed, one could argue that mixed models have had at least as great an impact in quantitative genetics as have molecular markers. A final important theme over the past 20 years has been the fusion of population and quantitative genetics, in particular the importance of coalescence theory with its applications for association mapping, scans for loci under selection, and estimation of the demography history of a population. What are the future directions of the field? While obviously important surprises await us, the general trend seems to be moving into higher and higher dimensional traits and, in general, dimensional considerations. We have methods to deal with infinite-dimensional traits indexed by a single variable (such as a trait varying over time), but the future will require us to treat much more complex objects, such as infinite-dimensional traits indexed over several variables and with graphs and dynamical networks. A second important direction is the interfacing of quantitative genetics with physiological and developmental models as a step towards both the gene–phenotype map as well as predicting the effects of environmental changes. The high-dimensional objects we will need to consider almost certainly have most of their variation residing on a lower (likely much lower) dimensional subspace, and how to treat these constraints will be an important area of future research. Conversely, the univariate traits we currently deal with are themselves projections of more complex structures onto a lower dimensional space, and simply treating these as univariate traits can result in serious errors in understanding their selection and biology. As a field, our future is quite bright. We have new tools and techniques, and (most importantly) new talent with an exciting international group of vibrant young investigators who have received their degrees since the last Congress. One cloud for concern, however, has been the replacement at many universities of plant and animal breeders with plant and animal molecular biologists. Molecular tools are now an integral part of breeding, but breeding is not an integral part of molecular biology.