Stem cells (SCs) are undifferentiated cells of multicellular organisms that can divide, self-renew, and differentiate. Despite the differences in their properties, the general principles of the existence of SCs can be distinguished in all multicellular organisms. In plants, SCs are found in meristems, structures that ensure the continuous growth of a plant and provide material for the formation of various specialized tissues. There are numerous types of meristems: shoot apical meristem (SAM) and root apical meristem (RAM), and lateral meristems (LMs) (procambium, cambium, and pericycle), as well as the so-called irregular meristems, developing under certain conditions (callus, meristems of symbiotic nodules, spontaneous and pathogen-induced tumors, etc.). Specific mechanisms of regulation, which are based on the interaction of plant hormones and the major groups of transcription factors, were identified for each meristem. The activity of meristems is determined by two opposing processes: proliferation and self-renewal of SCs in the central part of the meristem and differentiation of specialized cells in the periphery. WOX-CLAVATA systems are a regulatory component conservative for different meristems, which ensures the consistency of the composition of the meristem, as well as the balance of SC proliferation and differentiation. In this review, we consider the similarities and differences between the principles of the organization of SC niches in plants and animals, as well as in a variety of meristems of higher plants; special attention will be paid to the role of WOX-CLAVATA systems in maintaining meristems and their interaction with other meristem regulators.