Patient-specific somatic cell reprogramming is likely to have a large impact on medicine by providing a source of cells for disease modelling and regenerative medicine. Several strategies can be used to reprogram cells yet they are generally characterised by a low reprogramming efficiency, reflecting the remarkable stability of the differentiated state. Transcription factors, chromatin modifications, and non-coding RNAs can increase the efficiency of reprogramming. However, the success of nuclear reprogramming is limited by epigenetic mechanisms that stabilise the state of gene expression in somatic cells and thereby resist efficient reprogramming. We review here the factors that influence reprogramming efficiency, and especially those that restrict the natural reprogramming mechanisms of eggs and oocytes. We see this as a step towards understanding the mechanisms by which nuclear reprogramming takes place.