In this mini-symposium we discuss current analytical and computational developments in the investigation of nonlinear models found in biology. Including kinetic transport, integro-differential equations, structured population and stochastic models utilized to define complicated phenomena including neuronal dynamics, coagulation processes, biochemical proofreading, and epidemic distribution, the lectures include a wide spectrum of methods. The studies include the numerical analysis of age-structured neural models and their long-time behavior, the creation of flux-type solutions for the Smoluchowski coagulation equation, the influence of breaking detailed balance in stochastic kinetic proofreading systems, the significance of nonlocal aggregation in spatially heterogeneous epidemic models and pattern formation in confined populations of microswimmers. Collectively, these studies show how PDEs, functional analysis, stochastic methods, and numerical methods techniques can help to illuminate equilibrium structures, stability characteristics, and developing patterns in biological systems.