Owing to their original properties, pluripotent human embryonic stem cells (hESCs) and their progenies are highly valuable not only for regenerative medicine, but also as tools to study development and pathologies or as cellular substrates to screen and test new drugs. However, ensuring their genomic integrity is one important prerequisite for both research and therapeutic applications. Until recently, several studies about the genomic stability of cultured hESCs had described chromosomal or else large genomic alterations detectable with conventional karyotypic methods. In the past year, several laboratories have reported many small genomic alterations, in the megabase-sized range, using more sensitive karyotyping methods, showing that hESCs are prone to acquire focal genomic abnormalities in culture. As these alterations were found to be nonrandom, these findings strongly advocate for high-resolution monitoring of human pluripotent stem cell lines, especially when intended to be used for clinical applications