Many traits distinguish humans from their closest relatives, the great apes. Key examples include our extended learning period, upright walking and a 3-fold increase in brain size. However, the genetic basis for the overwhelming majority of human-specific traits remains unknown. This is primarily because most of the sequence variants that separate humans from great apes are found within non-coding regions of the genome, which makes it difficult to characterize their functional effects. Here, we use massively parallel reporter assays to test the functional effect of each of the variants that emerged in putative regulatory regions during human evolution. For each of these 541,851 single-nucleotide variants, we synthesized the human and ape allele and compared their effect on gene expression in two cell types (neurons and chondrocytes). We identified tens of thousands of variants that alter gene expression between humans and great apes, thus providing the first map of the variants that shaped human gene expression. We integrated this information with data on transcription factor motifs and various regulatory marks to uncover the molecular mechanisms underlying differential activity. In addition, we linked these variants to the genes they likely affect in their endogenous context, and studied which organs, pathways and phenotypes were particularly affected by these expression changes. Altogether, our work opens a window to study the complex relationship between sequence, expression and phenotype, and to investigate the evolutionary mechanisms and selective pressures that have shaped human adaptations.