Two finitely generated groups are abstractly commensurable if they have isomorphic finite-index subgroups. Classifying groups up to commensurability is a fundamental question in geometric group theory. I will discuss joint work with Emily Stark and Anne Thomas on the commensurability classification of a class of hyperbolic right-angled Coxeter groups. A key step in our proof is showing that these groups are virtually geometric amalgams of free groups.