During the last ten years we have discovered a tight link between gradient flows on one hand and large deviations on the other. Gradient flows are a class of dynamical systems: evolution equations driven by the 'fastest decrease' of an energy or entropy functional. Large deviation theorems give rigorous asymptotic characterizations of rare events of random variables.
These two unlikely bedfellows turn out to be closely related, in the case of evolution equations that arise as macroscopic, upscaled limits of stochastic processes. Such evolution equations arise in many physical processes: diffusion, heat conduction, fluid flow, elasticity, plasticity, chemical reactions, and many more. In this talk I will show how these two concepts relate to each other and to the underlying physics, chemistry, or biology. I also will show how it leads to a rigorous underpinning of a modelling methodology known as Variational Modelling, and in this way gives rise to new descriptions of the physical world around us.