This talk starts with a survey about hyperbolic volume in three dimensions, dilogarithms and zeta values.
The main part deals with similar features and questions about hyperbolic volume of (non-)arithmetic Coxeter orbifolds of higher dimensions. We discuss the volume problem for certain Coxeter pyramids. This family gives rise to interesting (non-)arithmetic reflection groups whose commensurability classification has recently been performed (joint work with R. Guglielmetti and M. Jacquemet).
This is a report about ongoing work.