Petri nets, invented by Carl Adam Petri in 1960, have been widely used in many areas ranging from computation theory, concurrency modeling, and software design to manufacturing automation, workflow analysis, and web service composition. As a modeling tool for discrete event dynamic systems, Petri nets play the same role as differential equation theory does in modeling dynamic continuous systems, difference equations in modeling digital control systems, and linear algebra in describing optimization problems with mathematical programming. This presentation intends to present Petri nets as a powerful modeling tool for discrete event dynamic systems. The most recent developments related to deadlock control methods are presented. Deadlock is a phenomenon in which a system or a part of it remains indefinitely blocked and cannot terminate its task. Such phenomenon often implies disaster in man-made systems and, therefore, must be carefully handled by system designers, analysts and engineers. Deadlock-free operations of automated systems in manufacturing and transportation are essential. The presentation will reveal the application of Petri nets to the deadlock control problem by focusing on two approaches: The first approach is based on the theory and concept of siphons. Siphons are structural objects in Petri nets. When siphons are prevented from being empty, the nets are deadlock-free and thus live for certain classes of Petri net models of automated manufacturing systems. The concepts of elementary siphons and dependent siphons are presented. Using these concepts a much simpler controller can be synthesized than the traditional siphon-based methods. To achieve the maximally permissive controller, an iterative method based on the reachability graph of the net model is outlined. All good and bad markings are identified and then the bad markings are eliminated by an iterative addition of place monitors and invariants. The advantages and disadvantages of these two approaches are presented and the challenging research issues are discussed.