The sequential formation of somites along the elongating zebrafish body axis is a model system for understanding the patterning of a growing tissue as well as the control of biological timing. We have used a combination of live imaging, gene expression analysis, and physical theory to explore the organization and function of the segmentation clock, the synchronized oscillating gene network that underlies the dynamics of somitogenesis. I will discuss new experimental results identifying the first somitogenesis period mutants, and corresponding theoretical approaches that explain the collective control of cellular oscillations at the tissue level in terms of the delays in the coupling between cells.