Many phenotypic traits of interest are heritable and vary as a function of genetic and external factors. Genome-wide association studies have revealed an abundance of individual genetic loci that are linked to phenotypes, including human diseases. Most recent large-scale studies have begun to complement genotype and phenotype data with readouts from high-throughput molecular profiling techniques, allowing studying intermediate genetic regulation at the level of transcription and translation. However, despite the success of initial studies, many challenges and open questions remain how these high-dimensional data can be analyzed most effectively. As demonstrated by recent work, batch effects, population structure and other confounding factors can both introduce spurious associations and preclude true biological relationships. Moreover, genetic effects are often specific to a particular external context such as the environmental state, which may not be known or measurable with sufficient precision. Despite their relevance, little is understood how these confounding and external factors affect the analyses and can be accounted for. In this talk, I will discuss recent computational approaches that build on statistical modelling to estimate these factors from the observed data to improve genetic studies.