Random processes acting through dynamical systems with thresholds lie at the heart of many natural and man-made phenomena. The thresholds here considered are general including not only sharp or “hard” boundaries but also a class of dynamical, nonlinear system functions some of which are themselves mediated by the noise. Processes include noise-induced transitions, postponed and advanced bifurcations, noise enhanced propagation of coherent structures, and stochastic resonance and synchronization. Examples of these processes are found in a wide range of disciplines from physics and chemistry to neuroscience and even human and animal behavior and perception. I will discuss some of these examples connecting them with their fundamental dynamical origins.