Circadian rhythms are a remarkable feature found in many disparate organisms across the planet, driving 24-hour oscillations in gene expression and behavior to align organism physiology with the day-night cycle. Perhaps two of the most fundamental questions in circadian biology are: how do these endogenous biological rhythms maintain a robust 24-hour periodicity, and what are the consequences if the clock fails to function correctly? To address these basic questions, in this work I and my colleagues turn to the model photosynthetic cyanobacterium Synechococcus elongatus, which possesses the simplest known circadian clock composed of only three proteins, KaiA, KaiB, and KaiC. In the main chapter of this dissertation, I investigate how molecular stochasticity impacts the precision of the cyanobacterial clock as a result of limited cellular Kai protein copy number, finding that high protein expression is required to suppress timing errors due to a noisy negative feedback loop in the oscillator. Additionally, I find that the molecular noise inherent in the feedback loop forces a smaller, related cyanobacterium to adopt a qualitatively different environmentally-driven timing strategy that is more optimal for a lower Kai copy number. The other two studies presented here are those in which I contributed as a co-author to investigate how the Kai oscillator maintains period robustness against fluctuations in protein stoichiometry as well as how timing mismatch between the clock and environment impacts the fitness of individual cyanobacterial cells. Lastly, I present an ongoing project that utilizes ancestral protein reconstruction techniques to determine whether the period of the Kai oscillator changed over geological time to match the changing period of the Earth’s rotation.