Human monozygotic (MZ) twins estimated to occur once in 250 live births, result from an errant decision by embryonic cell(s) to develop as separate embryos. They are considered genetically identical and any phenotypic discordance between them has been used to implicate the role of environment. More recent literature, however, has questioned these assumptions but the frequency and the nature of any genetic discordance between MZ twins remains poorly understood. We will review published cases of phenotypic and genetic discordance between monozygotic twins to argue that not all discordance between such twins is due to differences in environment. The causes of reduced concordance between MZ twins remains poorly understood. They represent among the challenging aspects of the genetics of complex multi-factorial traits and diseases. A number of questions regarding the published results on MZ twins merit a re-assessment in the light of modern molecular insight of the human genome. Such an assessment is needed in directing future studies on MZ twins. In particular, we will deal with the origin, development, genetic and epigenetic factors that may have implications in discordance of the MZ twin pairs.