The essential nature of meristematic tissues is addressed with reference to conceptual frameworks that have been developed to explain the behaviour of animal stem cells. Comparisons are made between different types of plant meristems with the objective of highlighting common themes that might illuminate underlying mechanisms. A more in depth comparison of the root and shoot apical meristems is made which suggests a common mechanism for maintaining stem cells. The relevance of organogenesis to stem cell maintenance is discussed, along with the nature of underlying mechanisms which help ensure that stem cell production is balanced with the depletion of cells through differentiation. Mechanisms that integrate stem cell behaviour in the whole plant are considered, with a focus on the roles of auxin and cytokinin. The review concludes with a brief discussion of epigenetic mechanisms that act to stabilise and maintain stem cell populations.