Interpreting the effects of genetic variants is key to understanding individual susceptibility to disease and designing personalized therapeutic approaches. Modern experimental technologies are enabling the generation of massive compendia of human genome sequence data and associated molecular and phenotypic traits, together with genome-scale expression, epigenomics and other functional genomic data. Integrative computational models can leverage these data to understand variant impact, elucidate the effect of dysregulated genes on biological pathways in specific disease and tissue contexts, and interpret disease risk beyond what is feasible with experiments alone. In this Review, we discuss recent developments in machine learning algorithms for genome interpretation and for integrative molecular-level modelling of cells, tissues and organs relevant to disease. More specifically, we highlight existing methods and key challenges and opportunities in identifying specific disease-causing genetic variants and linking them to molecular pathways and, ultimately, to disease phenotypes.