Studies using high-resolution genome-wide approaches have recently reported that genomic and epigenomic alterations frequently accumulate in human pluripotent cells. Detailed characterization of these changes is crucial for understanding the impact of these alterations on self-renewal and proliferation, and particularly on the developmental and malignant potential of the cells. Such knowledge is required for the optimized and safe use of pluripotent cells for therapeutic purposes, such as regenerative cellular therapies using differentiated derivatives of pluripotent cells.In this Review, we summarize the current knowledge of the genomic and epigenomic stability of pluripotent human cells and the implications for stem cell research.