This review highlights the years of research on the genetics of in vitro regeneration in higher plants conducted at the Department of Genetics and Biotechnology of Saint Petersburg State University. The genetic collection of radish (Raphanus sativus) created at the department by selfing of individual plants from three cultivars was used as a model in these studies. Some radish inbred lines from the genetic collection form spontaneous tumors in the roots and are also used to study mechanisms of tumor growth in higher plants. It was revealed that radish lines that differed in the ability to form tumors also contrastingly differed in the reaction of their explants to auxin and cytokinin in vitro, which reflects a difference in the levels of these hormones in the tissues of related tumorous and non-tumorous radish lines. Moreover, high concentrations of cytokinins in cultural medium induced tumor formation in the regenerated plants of tumorous radish lines. The presence of meristematic zones in spontaneous tumors in radish lines, as well as in crown gall tumors induced by Agrobacterium tumefaciens and cytokinin-induced tumors made it possible to reveal the role of the main meristem regulators, such as KNOX and WOX family transcription factors and the CLAVATA system, in both the process of tumor growth and regeneration in plants. Analysis of the expression of meristem-specific genes during the development of spontaneous and induced tumors in radish as well as in regenerated radish plants confirmed this assumption.