Synthetic microbial consortia combine multiple strains of engineered microbes to cooperatively bring about population-level phenotypes. The constituent strains can coordinate their behavior and display emergent behaviors that are difficult to engineer into isogenic populations. The design of consortia is more complex than that of single-strain synthetic systems. A mechanistic, mathematical description of the spatiotemporal dynamics of these microbial consortia is needed for progress. I will describe several mathematical approaches and challenges in this endeavor, including a recent successful design and mathematical model of a population level synthetic genetic oscillator. This is joint work with Matthew Bennett and his group at Rice University.