The ABS (atom-bond sum-connectivity) index is a topological index, that was introduced in 2022 by amalgamating the main ideas of two well-examined indices. Mathematical aspects (especially, extremal results and bounds) of the ABS index have already been studied considerably. The primary goal of this review paper is to collect known bounds and extremal results regarding the ABS index. Several new extremal results, which follow easily from existing general results, are also given. Moreover, a number of open problems and conjectures, arising from the reported results, are proposed.