The conjugated-circuit model is reviewed. The concept of conjugated circuits is presented and the resonance energy expression based on conjugated circuits is given. The selection of parameters for various kinds of conjugated circuits is described. The computational scheme for making conjugated-circuit calculations is detailed and several approaches to key combinatorial problems in the scheme, i.e. the enumeration of Kekul structures and the enumeration of conjugated circuits, are outlined. The polycyclic systems studied so far by the conjugated-circuit model are listed and this reveals a wide variety of structurally rather diverse systems ranging from benzenoid hydrocarbons to high-temperature superconductors. 1990.