Models of cellular processes are often represented with networks that describe the interactions between the constituent molecules. These networks are usually incredibly complex. However, hidden within the complexity there are sometimes underlying structures that, if properly quantified, give great insight into the dynamical or stationary behavior of the system. In this talk, I will give a broad overview of research in this direction. The dynamics of biochemical reaction systems can be modeled either deterministically or stochastically, and I will present results for each modeling choice (though most of the focus will be on the stochastic models). I will also present some open problems in the field and describe some applications of work related to stochastic models in the setting of theoretical computer science.