Pluripotent stem cells may acquire genetic and epigenetic variants during culture following their derivation. At a conference organized by the International Stem Cell Initiative, and held at The Jackson Laboratory, Bar Harbor, Maine, October 2016, participants discussed how the appearance of such variants can be monitored and minimized and, crucially, how their significance for the safety of therapeutic applications of these cells can be assessed. A strong recommendation from the meeting was that an international advisory group should be set up to review the genetic and epigenetic changes observed in human pluripotent stem cell lines and establish a framework for evaluating the risks that they may pose for clinical use. The International Stem Cell Initiative organized a conference to review current understanding of the detection, origins, and consequences of genetic and epigenetic variants that arise in cultures of human pluripotent stem cells. This report provides an overview of the discussions and a recommendation to form an advisory group to help reach an international consensus on risk assessment for clinical applications.