Almost all organisms have near 24-hour rhythms in physiology to anticipate changes associated with the day-night cycle. These rhythms are produced by circadian clocks which run independent of external signals. Cyanobacteria are the simplest organisms to have a circadian clock, consisting of three genes, KaiA, KaiB and KaiC. They form a biochemical oscillator which drives transcriptional rhythms across the entire genome, including the clock genes. Much is still unknown about how the sequence and structure of the three proteins determine key clock properties. In the first chapter of this thesis, I provide experimental and computational evidence supporting a novel model of feedback control in the cyanobacterial clock based the ability of the two KaiC phosphorylation sites to opposingly control KaiC binding at the oligomeric level to its activity modulators KaiA and KaiB. This provides a mechanism for the previously unexplained robustness in clock periodicity against changing component concentrations. In the second chapter, I describe the design and application of a deep sequencing based scanning mutagenesis screen to comprehensively define the sequence-function relationships of the Kai clock genes. Both chapters contribute novel insights into the biochemical workings of cyanobacterial circadian clock.