I will give an overview of my work in mathematical cell biology.  First I will discuss topics related to polarity, specifically in the context of cell movement.  This and numerous other cell functions require identification of a “front” and “back” (e.g. polarity).   In some cases this can form spontaneously and in others sufficiently large stimuli are required.  I will discuss a mechanistic theory for how cells might transition between these behaviors by modulating their sensitivity to external stimuli.  In order to address this and analyze the systems being presented, I will describe a new non-linear bifurcation technique, the Local Perturbation Analysis, for analyzing complex, spatial biochemical networks.  This methodology fills a void between simple (but limited) stability techniques and more thorough (but in many cases impractical) non-linear PDE analysis techniques.  Additionally, I will discuss work related to early development of the mammalian embryo.  A vital first step in this process is the formation of an early placenta prior to implantation.  I will discuss a multi-scale stochastic model of this spatial patterning event and show that genetic expression noise is both necessary and sufficient for this event to occur robustly.