The power of genome-wide association studies (GWAS) rests on several foundations: (i) there is a significant amount of additive genetic variation, (ii) individual causal polymorphisms often have sizable effects and (iii) they segregate at moderate-to-intermediate frequencies, or will be effectively 'tagged' by polymorphisms that do. Each of these assumptions has recently been questioned. (i) Why should genetic variation appear additive given that the underlying molecular networks are highly nonlinear? (ii) A new generation of relatedness-based analyses directs us back to the nearly infinitesimal model for effect sizes that quantitative genetics was long based upon. (iii) Larger effect causal polymorphisms are often low frequency, as selection might lead us to expect. Here, we review these issues and other findings that appear to question many of the foundations of the optimism GWAS prompted. We then present a roadmap emerging as one possible future for quantitative genetics. We argue that in future GWAS should move beyond purely statistical grounds. One promising approach is to build upon the combination of population genetic models and molecular biological knowledge. This combined treatment, however, requires fitting experimental data to models that are very complex, as well as accurate capturing of the uncertainty of resulting inference. This problem can be resolved through Bayesian analysis and tools such as approximate Bayesian computation-a method growing in popularity in population genetic analysis. We show a case example of anterior-posterior segmentation in Drosophila, and argue that similar approaches will be helpful as a GWAS augmentation, in human and agricultural research.