Sequence-based variation in gene expression is a key driver of disease risk. Common variants regulating expression in cis have been mapped in many expression quantitative trait locus (eQTL) studies, typically in single tissues from unrelated individuals. Here, we present a comprehensive analysis of gene expression across multiple tissues conducted in a large set of mono- and dizygotic twins that allows systematic dissection of genetic (cis and trans) and non-genetic effects on gene expression. Using identity-by-descent estimates, we show that at least 40% of the total heritable cis effect on expression cannot be accounted for by common cis variants, a finding that reveals the contribution of low-frequency and rare regulatory variants with respect to both transcriptional regulation and complex trait susceptibility. We show that a substantial proportion of gene expression heritability is trans to the structural gene, and we identify several replicating trans variants that act predominantly in a tissue-restricted manner and may regulate the transcription of many genes.