In recent times important progress has been made in the characterization and quantification of the notion of non-Markovianity for quantum dynamical evolutions. We will discuss this issue deriving in particular a large class of non-Markovian quantum dynamical maps arising as solution of memory kernel master equations. In the derivation one essentially builds on a quantization of results in classical probability theory. It appears that operator ordering plays an important role leading to a larger variety of behaviors in the quantum description. We will further show how such dynamics naturally appear within the framework of so-called collisional models.