A major goal of regenerative medicine is to produce cells to participate in the generation, maintenance, and repair of tissues that are damaged by disease, aging, or trauma, such that function is restored. The establishment of induced pluripotent stem cells, followed by directed differentiation, offers a powerful strategy for producing patient-specific therapies. Given how laborious and lengthy this process can be, the conversion of somatic cells into lineage-specific stem/progenitor cells in one step, without going back to, or through, a pluripotent stage, has opened up tremendous opportunities for regenerative medicine. However, there are a number of obstacles to overcome before these cells can be widely considered for clinical applications. Here, we focus on induced transdifferentiation strategies to convert mature somatic cells to other mature cell types or progenitors, and we summarize the challenges that need to be met if the potential applications of transdifferentiation technology are to be achieved.