Embryonic stem cells are characterized by their differentiation to all cell types during embryogenesis. In adult life, different tissues also have somatic stem cells, called adult stem cells, which in specific niches can undergo multipotent differentiation. The use of these adult stem cells has considerable therapeutic potential for the regeneration of damaged tissues. In both embryonic and adult stem cells, differentiation is controlled by epigenetic mechanisms, and the plasticity of differentiation in these cells is associated with transcription accessibility for genes expressed in different normal tissues. Abnormalities in genetic and/or epigenetic controls can lead to development of cancer, which is maintained by self-renewing cancer stem cells. Although the genetic abnormalities produce defects in growth and differentiation in cancer stem cells, these cells have not always lost the ability to undergo differentiation through epigenetic changes that by-pass the genomic abnormalities, thus creating the basis for differentiation therapy. Like normal stem cells, cancer stem cells can show plasticity for differentiation. This plasticity of cancer stem cells is also associated with transcription accessibility for genes that are normally expressed in different tissues, including tissues other than those from which the cancers originated. This broad transcription accessibility can also contribute to the behavior of cancer cells by overexpressing genes that promote cell viability, growth and metastasis.