How can the evolution of cosmic structures be understood? This question is important for cosmology in view of data analysis as well as for fundamental reasons. With this in mind, kinetic field theory (KFT) has been developed in recent years to study structure formation in ensembles of classical particles in and out of equilibrium. In a straightforward manner, KFT can be specialised to cosmology, where it allows to calculate highly non-linear power spectra of cosmic density fluctuations with analytic means. I will summarize the main concepts of KFT and its cosmological applications and show how the flexibility of KFT can be used to study structure formation with large varieties of dark-matter models or generalised theories of gravity.