The Ziegler spectrum of a ring \(R\) (the category of \(R\)-modules) [\textit{M. Ziegler}, Ann.\ Pure Appl.\ Logic 26, 149--213 (1984; Zbl 0593.16019)] is a topological space defined in terms of its category of modules. The authors investigate the relationship between the Ziegler spectrum of \(R\) and the associated triangulated category \(D(R)\). When \(R\) is a hereditary or von Neumann regular ring then the Ziegler spectrum of \(D(R)\) is a disjoint union of copies of the spectrum of \(R\). For general rings further indecomposable pure-injective objects of the category \(D(R)\) are necessary. A relation between the Ziegler spectrum of a quasi-Frobenius ring and that of its stable module category is studied as well.