Abstract: Impressive advances have recently been made on the derivation of kinetic equations. Yet the well-posedness and dynamics of these equations remain poorly understood. In this talk I will address such questions. First, I will present a method to prove global existence, scattering and propagation of moments of strong solutions for kinetic equations. I will discuss its implementation in concrete examples. Time permitting, I will also present negative results, namely ill-posedness for kinetic wave equations. This is based on joint work with Ioakeim Ampatzoglou.