Human embryonic stem cells (hESCs) are derived from human preimplantation embryos, and exhibit the defining characteristics of immortality and pluripotency. Indeed, these cell populations can be maintained for several years in continuous culture, and undergo hundreds of population doublings. hESCs are thus likely candidates for source of cells for cell replacement therapies. Although hESC lines appear stable in their expression of cytokine markers, expression of telomerase, ability to differentiate, and maintenance of a stable karyotype, several other aspects of stability have not yet been addressed, including mitochondrial sequencing, methylation patterns, and fine resolution cytogenetic analysis. Because of the potential utility of hESCs, it will be of utmost importance to evaluate the stability of these aspects of ESC biology.