There is a particularly interesting subset of Petri Nets -- (Extended) Free Choice Petri Nets that I actually fell in love with. If someone is interested in learning about them one of the best books on the subject is available here: http://www7.in.tum.de/~esparza/bookfc.html
There are some limitations of the model, but the theory is still fascinating (especially the duality property of Well-Formed PNs).