After a short historical introduction the role of Kekulé structures in theoretical chemistry is summarized. The present work concentrates upon conjugated hydrocarbons with six-membered rings. In a mathematical treatment they are represented by benzenoid systems, which consist of congruent regular hexagons. The vertices represent carbon atoms. Relations are given between certain characteristic numbers, viz. the number of vertices of different kinds (secondary, tertiary, external, internal), number of edges and of the rings. Kekuléan and non-Kekuléan benzenoids are exemplified. The latter class consists of mathematical constructions without any possible Kekulé structure. A great amount of work has been done in the area of graph theory applied to benzenoids. Some of the most important theorems are summarized. Another approach employs group theory in the studies of the symmetry of Kekulé structures. A benzenoid or one of its Kekulé structures may belong to one of the following eight symmetry groups: ▪ Examples are given. Cata-condensed benzenoids are defined by having no internal vertices. Especially simple are the single straight and single zig-zag chains. The number of Kekulé structures and their symmetries are treated in these two cases. In the latter case the Fibonacci numbers come in. Some classes of reticular benzenoids are defined, and the multiple zig-zag chains are considered in some detail. A recurrence formula for the number of Kekulé structures with relevance to this class of benzenoids is presented for the first time, along with several deductions from it.