Somatic embryogenesis (SE) is a process that scientists have been trying to understand for many years because, on the one hand, it is a manifestation of the totipotency of plant cells, so it enables the study of the mechanisms regulating this process, and, on the other hand, it is an important method of plant propagation. Using SE in basic research and in practice is invaluable. This article describes the latest, but also historical, information on changes in the chemical composition of the cell wall during the transition of cells from the somatic to embryogenic state, and the importance of symplasmic communication during SE. Among wall chemical components, different pectic, AGP, extensin epitopes, and lipid transfer proteins have been discussed as potential apoplastic markers of explant cells during the acquisition of embryogenic competence. The role of symplasmic communication/isolation during SE has also been discussed, paying particular attention to the formation of symplasmic domains within and between cells that carry out different developmental processes. Information about the number and functionality of plasmodesmata (PD) and callose deposition as the main player in symplasmic isolation has also been presented.