One of the most fascinating questions in evolutionary biology is how traits unique to humans, such as their high cognitive abilities, erect bipedalism, and hairless skin, are encoded in the genome. Recent advances in genomics have begun to reveal differences between the genomes of the great apes. It has become evident that one of the many mutation types, segmental duplication, has drastically increased in the primate genomes, and most remarkably in the human genome. Genes contained in these segmental duplications have a tremendous potential to cause genetic innovation, probably accounting for the acquisition of human-specific traits. In this review, I begin with an overview of the genes, which have increased their copy number specifically in the human lineage, following its separation from the common ancestor with our closest living relative, the chimpanzee. Then, I introduce the recent experimental approaches, focusing on SRGAP2, which has been partially duplicated, to elucidate the role of SRGAP2 protein and its human-specific paralogs in human brain development and evolution.