The shoot apical meristem of a flowering plant is the ultimate source of most of the above-ground cells that make up the plant. The meristem of Arabidopsis thaliana contains a few hundred cells that divide in precise patterns and in a precise geometry to maintain the meristem as cells depart from it to become differentiated parts of the plant, and to produce the spiral phyllotactic pattern of leaves and flowers. The activities of the meristem are therefore responsible for the architecture of the mature plant. We have developed new methods for imaging cells and gene activities in living meristems, by use of reporter gene constructs that mark changing patterns of gene expression by fluorescence, laser-scanning confocal microscopy, and computer-based image processing. We can observe all of the cell divisions, and changes in activity of reporter genes, in a single living meristem over several days. This has revealed the genetic basis for some of the meristematic activities, and is leading to computational models of cell number maintenance, and of phyllotaxis, in the Arabidopsis shoot.