Coxeter groups are groups of classical interest which arise naturally, for example as symmetry groups of regular tessellations of Euclidean or hyperbolic planes. Right-angled Coxeter groups form an important subclass: these have particularly simple presentations, and therefore provide a rich source of examples for testing conjectures in geometric group theory.  Yet despite their elementary descriptions, the spaces on which they act admit a surprising variety of geometries, making questions about their large-scale geometry very interesting.  I will introduce the questions of quasi-isometry and commensurability classification in geometric group theory, and describe the progress that has been made for right-angled Coxeter groups.  This will include joint work with A. Thomas and E. Stark.