Genetic networks that include positive and negative feedback can exhibit oscillations. These oscillations are a form of emergence, which is when novel patterns or properties arise during self organization of complex systems. Within the extending trunk and tail of the developing vertebrate embryo, the somitogenesis oscillator governs the periodic formation of segments that ultimately become the vertebral column and musculature. These oscillations occur within the context of noise created by cell movement, mitosis, and stochastic gene expression. Here, we review recent progress in our understanding of the role of the Notch signaling pathway in the zebrafish segmentation oscillator and our appreciation of how the oscillator interfaces with different sources of noise.