Plants produced vegetatively in tissue culture may differ from the plants from which they have been derived. Two major classes of off-types occur: genetic ones and epigenetic ones. This review is about epigenetic aberrations. We discuss recent studies that have uncovered epigenetic modifications at the molecular level, viz., changes in DNA methylation and alterations of histone methylation or acetylation. Various studies have been carried out with animals, and with plant cells or tissues that have grown in tissue culture but only little work has been done with shoots generated by axillary branching. We present various molecular methods that are being used to measure epigenetic variation. In micropropagated plants mostly differences in DNA methylation have been examined. Epigenetic changes are thought to underlie various well-known tissue-culture phenomena including rejuvenation, habituation, and morphological changes such as flower abnormalities, bushiness, and tumorous outgrowths in, among others, oil palm, gerbera, Zantedeschia and rhododendron.