With the exception of lymphocytes, the various cell types in a higher multicellular organism have basically an identical genotype but are functionally and morphologically different. This is due to tissue-specific, temporal, and spatial gene expression patterns which are controlled by genetic and epigenetic mechanisms. Successful cloning of mammals by transfer of nuclei from differentiated tissues into enucleated oocytes demonstrates that these genetic and epigenetic programs can be largely reversed and that cellular totipotency can be restored. Although these experiments indicate an enormous plasticity of nuclei from differentiated tissues, somatic cloning is a rather inefficient and unpredictable process, and a plethora of anomalies have been described in cloned embryos, fetuses, and offspring. Accumulating evidence indicates that incomplete or inappropriate epigenetic reprogramming of donor nuclei is likely to be the primary cause of failures in nuclear transfer. In this review, we discuss the roles of various epigenetic mechanisms, including DNA methylation, chromatin remodeling, imprinting, X chromosome inactivation, telomere maintenance, and epigenetic inheritance in normal embryonic development and in the observed abnormalities in clones from different species. Nuclear transfer represents an invaluable tool to experimentally address fundamental questions related to epigenetic reprogramming. Understanding the dynamics and mechanisms underlying epigenetic control will help us solve problems inherent in nuclear transfer technology and enable many applications, including the modulation of cellular plasticity for human cell therapies.