Cell and tissue plant cultures are used either to save vulnerable species from extinction or to multiply valuable genotypes, or both, and are widely applied for economically important plant species. For medicinal plants, the use of in vitro technologies for the production of secondary metabolites and pathogen-free plants has been greatly developed. Two opposite aspects characterize the in vitro micropropagation of medicinal plants: maintaining genetic fidelity for the perpetuation and preservation of elites, and the identification and exploitation of somaclonal variations associated with new, useful traits. A balance between what is advantageous and what is undesirable is necessary, and this implies the identification of somaclonal variability at all levels, from the phenotypic to molecular ones. This review addresses the somaclonal variation arising from the in vitro multiplication of medicinal plants from three perspectives: cytogenetics, genetics, and epigenetics. The possible causes of the appearance of somaclones, the methods for their identification, and the extent to which they are desirable are presented comparatively for different plant species with therapeutic properties. The emphasis is on the subtle changes at the genetic and epigenetic level, as it results from the application of methods based on DNA markers.