In this tutorial paper we survey some of the existing techniques for m
odelling, analysis and synthesis of asynchronous control circuits. All
these methods are based on the use of Petri nets as a tool for descri
bing the behaviour of such circuits. The descriptive power of Petri ne
ts allows them to model a wide range of asynchronous circuit component
s, whether they are built in the two-phase (micropipeline) or in the f
our-phase (logic gate based) design styles. We present three different
approaches to verification of net-based models, and show their relati
ve strengths and weaknesses. We advocate their complementary applicati
on for different classes of Petri nets and the properties verified. Tw
o major synthesis approaches are demonstrated using the example of a m
odulo-N Up/Down counter. The first one is a combination of Petri net l
evel decompositions and syntax-directed translation of nets into circu
its. The second one is based on logic synthesis from signal transition
graph specifications.