The circadian clock in the hypothalamus functions as an accurate timekeeper of physiological events by maintaining 24-hr periodic rhythms even in the presence of intrinsic and extrinsic perturbations. While many genes and proteins underlying the circadian clock have been identified, how they work together to generate robust rhythms remains unclear. This problem was selected as one of 125 important science puzzles for the present century by Science magazine. In this talk, I will discuss how mathematical modeling combined with experiments can reveal key molecular mechanisms that underlie robust rhythmicity in the face of perturbations, such as temperature change and external signals.