Permanent lines of pluripotent stem cells can be obtained from humans and monkeys using different techniques and from different sources--inner cell mass of the blastocyst, primary germ cells, parthenogenetic oocytes, and mature spermatogonia--as well as by transgenic modification of various adult somatic cells. Despite different origin, all pluripotent lines demonstrate considerable similarity of the major biological properties: active self-renewal and differentiation into various somatic and germ cells in vitro and in vivo, similar gene expression profiles, and similar cell cycle structure. Ten years of intense studies on the stability of different human and monkey embryonic stem cells demonstrated that, irrespective of their origin, long-term in vitro cultures lead to the accumulation of chromosomal and gene mutations as well as epigenetic changes that can cause oncogenic transformation of cells. This review summarizes the research data on the genetic and epigenetic stability of different lines of pluripotent stem cells after long-term in vitro culture. These data were used to analyze possible factors of the genome and epigenome instability in pluripotent lines. The prospects of using pluripotent stem cells of different origin in cell therapy and pharmacological studies were considered.