In contrast to animals, plants do not stop to initiate organs with the end of embryogenesis. Instead, most of the growth and development of higher plants will take place during later phases following germination of the seed. Plant development depends on the activity of two meristems, the root meristem and the shoot apical meristem (SAM), that are located at opposite ends of the plant embryo. These meristems serve as a source of pluripotent stem cells and, in case of the SAM, provide a centre for repetitive organ initiation. In order to maintain the SAM throughout plant life, the cells that are lost from the meristem through organ initiation and differentiation have to be replaced from the stem cell population. In this paper, we will discuss recent results indicating that the fate of stem cells in plant meristems is controlled by directional signalling systems.