Detailed mapping of genetic and environmental influences on the functional connectome is a crucial step toward developing intermediate phenotypes between genes and clinical diagnoses or cognitive abilities. We analyze resting-state data from two, adult twin samples - 390 twins from the Colorado Longitudinal Twin Sample and 422 twins from the Human Connectome Project - to examine genetic and environmental influence on all pairwise functional connections between 264 brain regions (~35,000 functional connections). Non-shared environmental influence was high, genetic influence was moderate, and shared environmental influence was weak-to-moderate across the connectome. The brain’s genetic organization is diverse and not as one would expect based solely on structure evident in non-genetically informative data or lower-resolution data. As follow-up, we make novel classifications of functional connections and examine highly-localized connections with particularly strong genetic influence. This high-resolution genetic taxonomy of brain connectivity will be useful in understanding genetic influences on brain disorders.