Abstract: There are four kinds of integer vectors arising from the structure theory of cluster algebras: $c$-vector, $d$-vector, $f$-vector and $g$-vector, which have played important roles in the study of cluster algebras. This paper is devoted to reviewing the concepts of those vectors and introducing their properties, research problems and research progress.

Key words: Cluster algebra, Denominator conjecture, $c$-vector, $f$-vector, $g$-vector