Precise genetic manipulation of human pluripotent stem cells will be required to realize their scientific and therapeutic potential. Here, we show that adeno-associated virus (AAV) gene targeting vectors can be used to genetically engineer human embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs). Different types of sequence-specific changes, including the creation and correction of mutations, were introduced into the human HPRT1 and HMGA1 genes (HPRT1 mutations being responsible for Lesch-Nyhan syndrome). Gene targeting occurred at high frequencies in both ESCs and iPSCs, with over 1% of all colony-forming units (CFUs) undergoing targeting in some experiments. AAV vectors could also be used to target genes in human fibroblasts that were subsequently used to derive iPSCs. Accurate and efficient targeting took place with minimal or no cytotoxicity, and most of the gene-targeted stem cells produced were euploid and pluripotent.