The spectral theory of Coxeter matrices has turned out to provide a powerful tool in the representation theory of finite dimensional algebras. The aim of this talk is to illustrate how preprojective algebras aid to understand spectral properties in the hereditary case. We examine the influence of quiver geometry on factorisations of Coxeter polynomials and entries of Coxeter eigenvectors. That way we derive classifications of spectral radii and some explicit constructions in terms of representation theoretical data from recent results on preprojective algebras. We give a short overview of other current approaches to this field and indicate how preprojective algebras may also be helpful in these areas.