Regenerative medicine offers the hope that cells for disease research and therapy might be created from readily available sources. To fulfil this promise, the cells available need to be converted into the desired cell types. We review two main approaches to accomplishing this goal: in vitro directed differentiation, which is used to push pluripotent stem cells, including embryonic stem cells or induced pluripotent stem cells, through steps similar to those that occur during embryonic development; and reprogramming (also known as transdifferentiation), in which a differentiated cell is converted directly into the cell of interest without proceeding through a pluripotent intermediate. We analyse the status of progress made using these strategies and highlight challenges that must be overcome to achieve the goal of cell-replacement therapy.