The aim of this work is the modeling and verification of concurrent systems subject to dynamic changes using extensions of Petri nets. We begin by introducing the notion of net rewriting system. In a net rewriting system, a system configuration is described as a Petri net and a change in configuration is described as a graph rewriting rule. We show that net rewriting systems are Turing powerful, that is, the basic decidable properties of Petri nets are lost and, thus, automatic verification in not possible for this class. A subclass of net rewriting systems are reconfigurable Petri nets. In a reconfigurable Petri net, a change in configuration amounts to the modification of the flow relations of the places in the domain of the involved rule according to this rule, independently of the context in which this rewriting applies. We show that reconfigurable Petri nets are formally equivalent to Petri nets. This equivalence ensures that all the fundamental properties of Petri nets are still decidable for reconfigurable Petri nets and this model is thus amenable to automatic verification tools. Therefore, the expressiveness of both models is the same, but, with reconfigurable Petri nets, we can easily and directly model systems that change their structure dynamically.