Abstract: For a group G with generating set S, a representative system R is a set of words in S such that every group element is uniquely represented by a word in R. Some representative systems are "nicer" than others, for instance, the (Cartesian) coordinate in abelian groups and the Mal'cev coordinate in nilpotent groups. In the 1990s, Brazil, and independently Collins, Edjvert, and Gill established a nice representative system for solvable Baumslag-Solitar groups and used it to show the rationality of the growth of the group. Such a system is a powerful combinatorial tool that has been applied to study other properties of the group, including conjugation curvature, conjugation growth, and solutions of equations in solvable Baumslag-Solitar groups. In this talk, we will discuss the representative systems for solvable Baumslag-Solitar groups and their applications. We will also discuss some other groups that admit a nice representative system.