Plants continuously generate organs at the flanks of their shoot apical meristems (SAMs). The patterns in which these organs are initiated, also called patterns of phyllotaxis, are highly stereotypic and characteristic for a particular species or developmental stage. This stable, predictable behaviour of the meristem has led to the idea that organ initiation must be based on simple and robust mechanisms. This conclusion is less evident, however, if we consider the very dynamic behaviour of the individual cells. How dynamic cellular events are coordinated and how they are linked to the regular patterns of organ initiation is a major issue in plant developmental biology.