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Cells generate various biological rhythms that control important aspects of cell physiology including circadian (daily) events, cell division, embryogenesis, DNA damage repair and metabolism. Since these cellular rhythms can determine the fitness or fate of organisms, how cells generate and control rhythms has become a central problem in biology. In this dissertation, we have developed theorems and mathematical models to understand how complex biochemical interactions of many genes and proteins generate and control biological rhythms over a wide range of conditions. In chapter 2, we have developed a mathematical theory that can infer biochemical interaction network of cellular clocks from timecourse data of gene and protein expression, which are relatively easy to be measured with the recent advances in experimental technology. We formulated this question as an existence and uniqueness problem and proved that the biochemical interaction network, and even biochemical rates, can sometimes uniquely be determined from only gene and protein timecourses. This theory provides a simple algorithm to determine whether two given species have a biochemical interaction. In chapter 3, we have found how cells generate rhythms with a constant period over a wide range of environmental conditions by studying circadian rhythms whose 24hr period is tightly regulated. By developing the most detailed and accurate mathematical model of circadian clock to date, we found that balancing a 1-1 stoichiometry between activators and repressors via double negative feedback loops is a key mechanism that tightly regulates the period of circadian rhythms. This mechanism provides an explanation for why various types of circadian disorders fail to regulate rhythms. In chapter 4, we considered rhythms of p53, one of the most important tumor suppressors. Unlike self-sustained circadian rhythms, p53 rhythms only occur in response to external stimuli such as DNA damage. Sustaining p53 rhythms is essential for p53 to repair DNA damage. By developing a mathematical model of p53 rhythms, we found that additional positive feedback loops via Rora and Cyt-c can significantly improve the sustainability of p53 rhythms in the presence of genetic heterogeneity and stochasticity.