Heritable variation in gene expression forms a crucial bridge between genomic variation and the biology of many traits. However, most expression quantitative trait loci (eQTLs) remain unidentified. We mapped eQTLs by transcriptome sequencing in 1012 yeast segregants. The resulting eQTLs accounted for over 70% of the heritability of mRNA levels, allowing comprehensive dissection of regulatory variation. Most genes had multiple eQTLs. Most expression variation arose from trans-acting eQTLs distant from their target genes. Nearly all trans-eQTLs clustered at 102 hotspot locations, some of which influenced the expression of thousands of genes. Fine-mapped hotspot regions were enriched for transcription factor genes. While most genes had a local eQTL, most of these had no detectable effects on the expression of other genes in trans. Hundreds of non-additive genetic interactions accounted for small fractions of expression variation. These results reveal the complexity of genetic influences on transcriptome variation in unprecedented depth and detail., eLife digest Every individual’s genome is unique, with variations in the DNA sequence at many thousands of points. Each difference is a change in one or more ‘letters’ of the DNA code. Some of these DNA letter variations have consequences for the way the individual looks or behaves. They can influence these traits either by changing the sequence of a protein encoded by a gene; or by changing when, where or how much a gene is active. Studying how individual differences in the DNA influence gene activity requires a very large amount of data on many individuals within a species. Only recently have such large datasets become available. These have made it possible to study these regulatory differences in unprecedented detail. Albert, Bloom et al. set out to map as many regulatory genetic variants as possible in budding yeast – a popular model organism used in many branches of science. The approach involved measuring how active every gene in the genome was, and which genetic variants influenced whether each gene’s activity was turned up or down, in more than 1,000 different strains of yeast. Thousands of regions of the DNA turned out to influence regulation of genes. The analysis revealed that almost every gene is influenced by a complex set of regulatory regions all over the genome. Some hotspot regions were found to influence thousands of genes at once. The findings provide the most complete set of data for studying the effects of variation in DNA sequence on genetic regulation in any species, and can act as a model for researchers to carry out similar experiments in other species. Ultimately, these results could help understand exactly how differences in genome sequence help to make individuals unique.