Abstract: A finitely generated group can be endowed with a natural metric which is unique up to coarse isometries, or quasi-isometries. A fundamental question is to classify finitely generated groups up to quasi-isometry. Commensurability is an algebraic property of pairs of groups which implies quasi-isometry, but is stronger in general. I will talk about the quasi-isometry and commensurability classification of a class of hyperbolic right-angled Coxeter groups. This is work in progress with Anne Thomas.