Based on the general concept of slow manifold of dynamical system and its mathematical description, the authors discuss systematically the existence and some general properties of slow manifold in atmospheric dynamics. The discussion emphasizes particularly on some important issues closely related to the slow manifold of the atmospheric motion such as properties of the balance dynamics, the spontaneous emission of inertia gravity wave from balance flow, theory and application of PV inversion and the relation to initialization issue of numerical model. Moreover, an overview of the history and the state of the art of researches in this field are given to provide domestic researchers of relevant topics a clue for the understanding of general picture of this field and entering into specific research issues.