The potential of human induced pluripotent stem cells (iPSCs) to self-renew indefinitely and to differentiate virtually into any cell type in unlimited quantities makes them attractive for in vitro disease modeling, drug screening, personalized medicine, and regenerative therapies. As the genome of iPSCs thoroughly reproduces that of the somatic cells from which they are derived, they may possess genetic abnormalities, which would seriously compromise their utility and safety. Genetic aberrations could be present in donor somatic cells and then transferred during iPSC generation, or they could occur as de novo mutations during reprogramming or prolonged cell culture. Therefore, to warrant the safety of human iPSCs for clinical applications, analysis of genetic integrity, particularly during iPSC generation and differentiation, should be carried out on a regular basis. On the other hand, reprogramming of somatic cells to iPSCs requires profound modifications in the epigenetic landscape. Changes in chromatin structure by DNA methylations and histone tail modifications aim to reset the gene expression pattern of somatic cells to facilitate and establish self-renewal and pluripotency. However, residual epigenetic memory influences the iPSC phenotype, which may affect their application in disease therapeutics. The present review discusses the somatic cell origin, genetic stability, and epigenetic memory of iPSCs and their impact on basic and translational research.