Petri nets are one of the most popular formal models for the representation and analysis of parallel processes. They are due to C. A. Petri, who introduced them in his doctoral dissertation in 1962. Some years later, and independently from Petri’s work, R. M. Karp and R. E. Miller introduced vector addition systems [ J. Comput. Syst. Sci. 3, 147-195 (1969; Zbl 0198.326)], a simple mathematical structure which they used to analyse the properties of ‘parallel program schemata’, a model for parallel computation. In their seminal paper on parallel program schemata, Karp and Miller studied some decidability issues for vector addition systems, and the topic continued to be investigated by other researchers. When Petri’s ideas reached the States around 1970, it was observed that Petri nets and vector addition systems were mathematically equivalent, even though their underlying philosophical ideas were rather different (a computational approach to the physical world in Petri’s view, a formal model for concurrent programming in Karp and Miller’s). This gave more momentum to the research on decidability questions for Petri nets, which has since continued at a steady pace.