Genetic variation influencing gene expression and splicing is a key source of phenotypic diversity. Though invaluable, studies investigating these links in humans have been strongly biased toward participants of European ancestries, diminishing generalizability and hindering evolutionary research. To address these limitations, we developed MAGE, an open-access RNA-seq data set of lymphoblastoid cell lines from 731 individuals from the 1000 Genomes Project spread across 5 continental groups and 26 populations. Most variation in gene expression (92%) and splicing (95%) was distributed within versus between populations, mirroring variation in DNA sequence. We mapped associations between genetic variants and expression and splicing of nearby genes (cis-eQTLs and cis-sQTLs, respective), identifying >15,000 putatively causal eQTLs and >16,000 putatively causal sQTLs that are enriched for relevant epigenomic signatures. These include 1310 eQTLs and 1657 sQTLs that are largely private to previously underrepresented populations. Our data further indicate that the magnitude and direction of causal eQTL effects are highly consistent across populations and that apparent "population-specific" effects observed in previous studies were largely driven by low resolution or additional independent eQTLs of the same genes that were not detected. Together, our study expands understanding of gene expression diversity across human populations and provides an inclusive resource for studying the evolution and function of human genomes.