Conversion of somatic cells to pluripotency by defined factors is a long and complex process that yields embryonic-stem-cell-like cells that vary in their developmental potential. To improve the quality of resulting induced pluripotent stem cells (iPSCs), which is important for potential therapeutic applications, and to address fundamental questions about control of cell identity, molecular mechanisms of the reprogramming process must be understood. Here we discuss recent discoveries regarding the role of reprogramming factors in remodelling the genome, including new insights into the function of MYC, and describe the different phases, markers and emerging models of reprogramming.