A central question of biology is the basis of stable cell fates. Cell fates are formed during development, where the zygote progresses from totipotency to terminal differentiation. Each step of lineage commitment involves establishment of stable states encoding-specific developmental commitments that can be faithfully transmitted to daughter cells — a ‘memory’ of cell fate is acquired. However, this cell-fate memory is reversible and can be changed when experimental reprogramming procedures such as nuclear transfer to eggs or transcription factor overexpression are used. The ability to reprogram cell fates impacts regenerative medicine, as progress in understanding underlying molecular mechanisms of cell-fate changes can allow the generation of any cell type needed for cell replacement therapies. Given its potential, studies are currently aiming at improving the low efficiency of cell-fate conversion. In recent years, epigenetic mechanisms suggested to promote stable cell-fate memory emerged as factors that cause resistance to cell-fate conversions during nuclear reprogramming. In this review, we highlight the latest work that has characterised epigenetic barriers to reprogramming which, during normal development, help to maintain the stable differentiation status of cells.