The broad applications of somatic embryogenesis, both in basic and applied research, have stimulated studies on the determination of in vitro conditions for the induction of somatic embryos and their conversion into plants. As a result, efficient protocols on SE induction and plant regeneration have recently become available for many plant species, including Arabidopsis thaliana (L.) Heynh., a model plant in genetics and embryogenesis. Studies on factors controlling in vitro plant morphogenesis are highly desirable not only for the development of improved regeneration systems, but also for the analysis of molecular mechanisms underlying plant embryogenesis. This review focuses on the conditions influencing the induction of embryogenic potential in in vitro cultured plant cells. The roles of explant type, endo- and exogenous plant growth regulators and stress factors in the induction of somatic embryogenesis are especially emphasized. Possible mechanisms by which different factors induce or modify embryogenic competence in cultured plant cells are also discussed. Since the production of genetically solid and true-to-type plants is desired, especially for transformation and micropropagation practice, the problem of the genetic characteristics of regenerants, in terms of their chimerism and somaclonal variation, is discussed in some detail. Special consideration is given to A. thaliana– a major model plant species for classical genetics and genomics. Recent availability of efficient embryogenic cultures in this organism makes it possible to benefit from advanced genomic research of Arabidopsis to study plant embryogenesis on the molecular level.