It has been nearly 300 years since the first scientific demonstration of a self-sustaining circadian clock in plants. It has become clear that plants are richly rhythmic, and many aspects of plant biology, including photosynthetic light harvesting and carbon assimilation, resistance to abiotic stresses, pathogens, and pests, photoperiodic flower induction, petal movement, and floral fragrance emission, exhibit circadian rhythmicity in one or more plant species. Much experimental effort, primarily, but not exclusively in Arabidopsis thaliana, has been expended to characterize and understand the plant circadian oscillator, which has been revealed to be a highly complex network of interlocked transcriptional feedback loops. In addition, the plant circadian oscillator has employed a panoply of post-transcriptional regulatory mechanisms, including alternative splicing, adjustable rates of translation, and regulated protein activity and stability. This review focuses on our present understanding of the regulatory network that comprises the plant circadian oscillator. The complexity of this oscillatory network facilitates the maintenance of robust rhythmicity in response to environmental extremes and permits nuanced control of multiple clock outputs. Consistent with this view, the clock is emerging as a target of domestication and presents multiple targets for targeted breeding to improve crop performance.