Cell identity is a reflection of a cell type-specific gene expression profile, and consequently, cell type-specific transcription factor networks are considered to be at the heart of a given cellular phenotype. Although generally stable, cell identity can be reprogrammed in vitro by forced changes to the transcriptional network, the most dramatic example of which was shown by the induction of pluripotency in somatic cells by the ectopic expression of defined transcription factors alone. Although changes to cell fate can be achieved in this way, the efficiency of such conversion remains very low, in large part due to specific chromatin signatures constituting an epigenetic barrier to the transcription factor-mediated reprogramming processes. Here we discuss the two-way relationship between transcription factor binding and chromatin structure during cell fate reprogramming. We additionally explore the potential roles and mechanisms by which histone variants, chromatin remodelling enzymes, and histone and DNA modifications contribute to the stability of cell identity and/or provide a permissive environment for cell fate change during cellular reprogramming.