In 2016, a symposium was convened in Leroy C. Stevens' honor, in association with a meeting of the International Stem Cell Initiative (ISCI). ISCI, funded internationally, is composed of a group of ~100 scientists from many countries, under the leadership of Peter Andrews, who have worked together to characterize a significant number of human pluripotent stem cell lines, to monitor their genetic stability and their differentiation into mature cell types and tissues in vitro and in vivo. Those at the ISCI meeting puzzled through one of the thorniest problems in the therapeutic use of the differentiated derivatives of pluripotent stem cells for human therapy; namely, pluripotent stem cells can differentiate into any cell type in the adult organism, but they also have the capacity for unlimited self-renewal, hence if mutated they may have tumorigenic potential. The meeting considered how these cells might become genetically or epigenetically abnormal and how the safety of these cells for human therapeutic uses could be assessed and assured. The symposium was an opportunity to pay tribute to Leroy Stevens and to the basic science origins of this newest aspect of regenerative medicine. It was a time to reflect on the past and on how it can influence the future of our field.