Genomes contain a large number of genes that do not have recognizable homologues in other species. These genes, found in only one or a few closely related species, are known as orphan genes. Their limited distribution implies that many of them are probably involved in lineage-specific adaptive processes. One important question that has remained elusive to date is how orphan genes originate. It has been proposed that they might have arisen by gene duplication followed by a period of very rapid sequence divergence, which would have erased any traces of similarity to other evolutionarily related genes. However, this explanation does not seem plausible for genes lacking homologues in very closely related species. In the present article, we review recent efforts to identify the mechanisms of formation of primate orphan genes. These studies reveal an unexpected important role of transposable elements in the formation of novel protein-coding genes in the genomes of primates.