A major task in the provision of energy is the balancing of supply and demand. To be able to balance them, there has to be some kind of flexibility, including not only the generation or storage but also the consumption of energy. Therefore, realizing measures of demand side management calls for a suitable abstraction of flexibility, a.o., to allow for aggregation and to obtain intended flexible load shapes. However, the formalization of flexibility is a non-trivial problem and there are many different approaches not only in the literature but also in research projects, such as C/sells, ENSURE, and Advanced Decentral Grid Control. This paper analyzes given approaches, e.g., with respect to their usability in decentralized, cellular, and multi-modal energy grids. The major contribution of this paper is the proposal of a general definition of the term flexibility and the categorization of different approaches to the representation and coordination of flexibility in smart grids, including important aspects concerning communication and coordination.