The generation of induced pluripotent stem cells (iPSCs) from adult somatic cells is one of the most exciting discoveries in recent biomedical research. It holds tremendous potential in drug discovery and regenerative medicine. However, a series of reports highlighting genomic instability in iPSCs raises concerns about their clinical application. Although the mechanisms cause genomic instability during cellular reprogramming are largely unknown, several potential sources have been suggested. This review summarizes current knowledge on this active research field and discusses the latest efforts to alleviate the genomic insults during cellular reprogramming to generate iPSCs with enhanced quality and safety.