Monozygotic twins (MZ) are rarely absolutely "identical." This review discusses the types of genetic/epigenetic and prenatal environmental post-zygotic mechanisms that cause discordance within such twin pairs. Some of these mechanisms--ranging from heterokaryotypia to skewed X-chromosome inactivation--may cause extreme discordance, but these extremes are merely the more emphatic examples of discordance that, to some degree, underlies the majority of MZ twin pairs. Because of the entrenched misconception that MZ twins are necessarily identical, many MZ twin pairs are mistakenly designated as dizygotic (DZ). Clinical benefits to accurate zygosity determination include correct solid organ transplantation matching, if one twin requires donation for a non-genetically mediated disease; the opportunity of preventive management for disorders that do not manifest synchronously; and better counseling to parents regarding their individually unique, and often psychologically puzzling, twin offspring. In twin pairs with complex and confusing biological origins, more detailed zygosity testing may be required. For example, intermediate trigametic and tetragametic chimeric dizygotic twins are reviewed, some of whom are, nevertheless, monochorionic (MC). Because of inter-fetal vascular anastomoses in MC twins, genetic results from blood samples may not accurately reflect discordance in solid organs. Previously, it was thought that MZ twinning was some sort of embryological fluke. However, familial monozygotic twinning is more common than suggested by the literature. Seven new families are presented in an accompanying paper. Despite the difficulties and dangers of twin pregnancy (especially so for MC twins), human twinning persists, and continues to both challenge and fascinate parents, clinicians and geneticists. Copyright 2009 Wiley-Liss, Inc.