The integration of modern neuroimaging methods with genetically informative designs and data can shed light on the molecular mechanisms underlying the structural and functional organisation of the human connectome. Here, we review studies that have investigated the genetic basis of human brain network structure and function through three complementary frameworks: (1) the quantification of phenotypic heritability through classical twin designs; (2) the identification of specific DNA variants linked to phenotypic variation through association and related studies; and (3) the analysis of correlations between spatial variations in imaging phenotypes and gene expression profiles through the integration of neuroimaging and transcriptional atlas data. We consider the basic foundations, strengths, limitations, and discoveries associated with each approach. We present converging evidence to indicate that anatomical connectivity is under stronger genetic influence than functional connectivity and that genetic influences are not uniformly distributed throughout the brain, with phenotypic variation in certain regions and connections being under stronger genetic control than others. We also consider how the combination of imaging and genetics can be used to understand the ways in which genes may drive brain dysfunction in different clinical disorders.