This talk was part of the Graduate School on "Non-equilibrium Processes in Physics and Biology" held at the ESI August 19 -- 30, 2024.

I will cover a statistical-physics approach to describe colloidal suspensions and systems of active particles, the integration-through transients (ITT) framework. We will look at the fundamentals of nonequilibrium stochastic processes, the derivation of exact equations for the nonlinear response in such systems, and apply this to two different cases: Brownian particles under shear (time permitting also crossing the scales from a microscopic description to macroscopic flow laws), as well as active Brownian particles and its variants (as representatives of biophysical model systems for collective effects in microswimmers such as bacteria). As an outlook, some rocket science.