In this review we discuss how synthetic biology facilitates the task of investigating genetic circuits that are observed in naturally occurring biological systems. Specifically, we give examples where experimentation with synthetic gene circuits has been used to understand four fundamental mechanisms intrinsic to development and disease: multistability, stochastic gene expression, oscillations, and cell-cell communication. Within each area, we also discuss how mathematical modeling has been employed as an essential tool to guide the design of novel gene circuits and as a theoretical basis for exploring circuit topologies exhibiting robust behaviors in the presence of noise.