Recent developments in the identification, in vitro culture and differentiation of stem cells point to the unprecedented potential of these cells, or their derivatives, to cure degenerative disorders. Human embryonic stem cells (hESC) offer the particular advantage of prolonged proliferative capacity and great versatility in the lineages that can be formed in culture. Translating these advantages into clinical benefits faces many challenges, including efficient differentiation into the desired cell type(s), maintaining genetic stability during long-term culture and, finally, ensuring the absence of potentially tumorigenic hESC from the final product. It is this final safety issue that will form the focus of this review.