Pluripotent stem cells (PSCs) must maintain their proper genomic content in order to preserve appropriate self-renewal and differentiation capacities. However, their prolonged in vitro propagation, as well as the environmental culture conditions, present serious challenges to genome maintenance. Recent work has been focused on potential means to alleviate the genomic insults experienced by PSCs, and to detect them as soon as they arise, in order to prevent the detrimental consequences of these genomic aberrations on PSC application in basic research and regenerative medicine.