Genetic-epidemiological studies on monozygotic (MZ) twins have been used for decades to tease out the relative contributions of genes and the environment to a trait. Phenotypic discordance in MZ twins has traditionally been ascribed to non-shared environmental factors acting after birth, however recent data indicate that this explanation is far too simple. In this paper, we review other reasons for discordance, including differences in the in utero environment, genetic mosaicism, and stochastic factors, focusing particularly on epigenetic discordance. Epigenetic differences are gaining increasing recognition. Although it is clear that in specific cases epigenetic alterations provide a causal factor in disease etiology, the overall significance of epigenetics in twin discordance remains unclear. It is also challenging to determine the causality and relative contributions of environmental, genetic, and stochastic factors to epigenetic variability. Epigenomic profiling studies have recently shed more light on the dynamics of temporal methylation change and methylome heritability, yet have not given a definite answer regarding their relevance to disease, because of limitations in establishing causality. Here, we explore the subject of epigenetics as another component in human phenotypic variability and its links to disease focusing particularly on evidence from MZ twin studies.