The revolution of molecular biology in the early 1980s has revealed that biological systems consist of non-linear and stochastic biochemical interactions among many molecules. To understand such complex systems, mathematical modeling has been an invaluable tool. In this talk, I will introduce the typical process of mathematical modeling including mathematical representation, model fitting to data, analysis and simulations, and experimental validation with an example of circadian rhythms. Across each step of the modeling process, I will also describe our efforts to develop new mathematical tools and point to the parts of the current tool box of mathematical biology that need further mathematical development. Speaker(s): Jae Kyoung Kim (KAIST)