In this talk, we will discuss two parameterizations of the divisorial valuations of a higher dimensional function field using cohomology, while highlighting the connections with model theory. The first parameterization uses information from the combinatorial geometry associated to relative algebraic closure in the given function field, while the second uses the Galois action of a sufficiently global field on the cohomology theory in question. Some recent applications in birational anabelian geometry will also be discussed.