A variety of biological systems, including the circadian clock, heartbeat, and cell cycle, display rhythmic oscillating activities. Early genetic studies have identified central genes required for these biological oscillators and have mapped out the underlying molecular interaction networks. While these biological oscillators have distinct functions and utilize different genes and proteins, the central network architectures of the oscillators are highly conserved. This suggests that network structure is key in determining the properties of biological oscillators. In my graduate study, I have been investigating the fundamental design principles shared among biological oscillators. I first systematically analyzed the network structures of biological oscillators in a theoretical framework. This work identified novel network structures that affect robustness (resistance to environmental perturbations) and tunability (ability to change frequency), both are key properties of oscillator functions. To further study the function of these newly-identified network structures, I have developed an artificial cell system that reconstitutes robust cell cycle oscillations in cell free droplets. Importantly, this system is amenable to high-throughput single-droplet analysis and precise control of various experimental manipulations. I have further used this system to test predictions from my computational works and explored the mechanisms of cell cycle regulation. Combining both theoretical and experimental work on the biological oscillators, my PhD study identified novel mechanisms that fine-tune biological oscillators. These discoveries provide valuable insights to understand biological oscillator functions and may inspire new understanding of diseases caused by deficiencies in biological oscillators.