Let $G=(V,E)$ be a simple undirected and connected graph on $n$ vertices. The Graovac-Ghorbani ($AB{C}_{GG}$) index of a graph $G$ is defined as $$AB{C}_{GG}(G)=\sum _{uv\in E}\sqrt{\frac{n(u)+n(v)-2}{n(u)n(v)}},$$ where $n(u)$ is the number of vertices closer to vertex $u$ than vertex $v$ and $n(v)$ is defined analogously. This paper is a survey of topological Graovac-Ghorbani index of a graph $G$. It contains results on $AB{C}_{GG}$ which are known until this moment and some conjectures.