Atmospheric dynamics in the mid-latitudes features quasi-stationary atmospheric states (QSAS),  also denoted as atmospheric blocking. Despite the existence of a multitude of data-driven  approaches for their identification, a unified mathematical characterization of such states and  the conditions leading to transitions between them is still lacking. We aim to remedy this by  describing and analysing QSAS as persistent dynamical structures both in nonautonomous  deterministic dynamical models and nonstationary non-deterministic dynamical models. This dual view is expected  to elucidate different aspects of the cause, the persistence, and the predictability of QSAS.