My presentation will be focused on some mathematical methods used in the study of gene regulation, which refers to the complex network of molecular interactions by which cells control which genes are expressed in response to changing environmental conditions. I will also provide an introduction to the field of systems biology and an overview of the important roles that dynamical modeling and inverse problems have in efforts to understand gene regulation from a genome-wide perspective. I will use examples from my previous work studying mechanisms of gene regulation in fungi and in mammals to illustrate the role of dynamical modeling in systems biology. As an example of an inverse problem in systems biology, I will discuss my recent work in studying gene regulation in macrophages in atherosclerosis, using data integration and machine-learning methods. The amount of prior biology background required for this presentation will be less than epsilon.