Genome sequencing projects are discovering millions of genetic variants in humans, and interpretation of their functional effects is essential for understanding the genetic basis of variation in human traits. Here we report sequencing and deep analysis of messenger RNA and microRNA from lymphoblastoid cell lines of 462 individuals from the 1000 Genomes Project--the first uniformly processed high-throughput RNA-sequencing data from multiple human populations with high-quality genome sequences. We discover extremely widespread genetic variation affecting the regulation of most genes, with transcript structure and expression level variation being equally common but genetically largely independent. Our characterization of causal regulatory variation sheds light on the cellular mechanisms of regulatory and loss-of-function variation, and allows us to infer putative causal variants for dozens of disease-associated loci. Altogether, this study provides a deep understanding of the cellular mechanisms of transcriptome variation and of the landscape of functional variants in the human genome.