The last thirty years have seen a revolution in tracking data of biological agents across unprecedented spatial and temporal scales. From fluorescence microscopy to GPS devices placed in tracking collars, we know more about the moment-to-moment movement patterns of microparticles, microorganisms, and animals than ever before. And yet, in our standard applied math courses -- through partial differential models that use diffusion terms, in particular -- we treat these diverse agents as though they all follow the same rules of Brownian motion, essentially asserting that movement in different increments of time are always independent of each other. There are very good pedagogical and mathematical reasons to do this, but as our collaborations with biologists deepen, it is important to recognize that Brownian motion models often fail to capture fundamental drivers of movement behavior. All of this new data presents an exciting opportunity for mathematicians. *And, to abuse a sentiment from Tolstoy: every trajectory in the Brownian class is essentially the same, but every anomalous departure from the Brownian regime is anomalous in its own way.* In the details of the non-Brownian statistics lie vital clues to fundamental physical and physiological mechanisms of transport and interaction in living systems. Despite the wealth of new data, we still cannot see everything needed to explain why agents move the way they do. Often we are missing important context from the environment, or signals arriving from other agents in the system. Collaboration between experimentalists and mathematicians naturally emerges these in places where the dynamics of interest are intrinsically stochastic, but our ability to observe them is limited. How can we extract the maximum amount of information from a constrained field of view? How can we extrapolate this information from the brief window of the experimental platform to real-life time scales of biological function or dysfunction? How can we design experiments that reveal system properties discovered from mathematical modeling to be critical for determining outcomes? These questions animate the vast majority of my research, and this is why I feel so thankful for my varied collaborations theoreticians, statisticians, and experimentalists. My collaborators have varied scientific interests, but at the core of each interaction is a unique stochastic dynamic and a clear question driving our investigation: - How do the movement statistics of fluctuating microparticles inform us about material properties of the fluid in which they are immersed? - How can studying individual segments of piecewise ballistic intracellular cargo paths inform the distribution of material throughout biological cells, and how would this change when the function and arrangements of molecular motors are perturbed? - How can internal feedback mechanisms and control at dendritic boundaries both maintain the stunningly stable distribution of microtubule polarity in healthy cells, and yet also allow neurons to be rapidly responsive to axonal injury? - How do spatial patterns among corals in the ocean emerge from feedback dynamics with their inhabitants who can be either beneficial and deleterious for coral growth? - What is a naturally emergent family of probability distributions that can be used to characterize income inequality and quantify economic mobility? The tools required to pursue these questions involve a range of techniques, from mathematical and statistical theory, to numerical simulation, to inference from existing biological observations, to collaborative experimental design. Often, multiple stochastic models are capable of explaining a set of observations, but one is much more effective, or even elegant, in its ability to explain. We make explicit efforts toward rigorous model selection, not only studying which model provides the best and most useful fit, but also expressing our degree of uncertainty. In each case, stochastic modeling plays an essential role, but I am particularly drawn to systems in which assumptions that underlie the mathematical state-of-the-art are violated. In this way, innovation is required in all phases of the investigation, and importantly, the contribution of a mathematician is essential.