Discrete Event Systems (DES) are a special type of dynamic systems. The "state" of these systems changes only at discrete instants of time and the term "event" is used to represent the occurrence of discontinuous changes (at possibly unknown intervals). Different Discrete Event Systems models are currently used for specification, verification, synthesis as well as for analysis and evaluation of different qualitative and quantitative properties of existing physical systems. The main focus of this paper is the presentation of the automata and formal language model for DES introduced by Raniadge and Wonham in 1985. This model is suitable for the examination of some important control theoretic issues, such as controllability and observability from the qualitative point of view, and provides a good basis for modular synthesis of controllers. We will also discuss an Extended State Machine and Real-Time Temporal Logic model introduced by Ostroff and Wonham in [OW87]. It incorporates an explicit notion of time and means for specification and verification of discrete event systems using a temporal logic approach. An attempt is made to compare this model of DES with other ones.