Abstract
The atom-bond connectivity (ABC) index was introduced in the last quarter of the 1990s to improve the prediction power of the Randie index. Later on, in 2008, the factor root 2 was dropped from the original definition of the ABC index, and some additional chemical applications of this index were reported, which resulted in considerable interest in studying the mathematical properties of the ABC index. There are more than a hundred papers devoted to the mathematical aspects of this graph invariant. The primary purpose of this review is to gather the existing bounds and extremal results concerning the ABC index.