Human pluripotent stem cells (hPSCs) can acquire non-random genomic variation during culture. Some of these changes are common in tumours and confer a selective growth advantage in culture. Additionally, there is evidence that reprogramming of human induced pluripotent stem cells (hiPSCs) introduces mutations. This poses a challenge to both the safety of clinical applications and the reliability of basic research using hPSCs carrying genomic variation. A number of methods are available for monitoring the genomic integrity of hPSCs, and a balance between practicality and sensitivity must be considered in choosing the appropriate methods for each use of hPSCs. Adjusting protocols by which hPSCs are derived and cultured is an evolving process that is important in minimising acquired genomic variation. Assessing genetic variation for its potential impact is becoming increasingly important as techniques to detect genome-wide variation improve.