The monodromy conjecture of Denef—Loeser is a conjecture in singularity theory that predicts that given a complex polynomial f, and any pole s of its motivic zeta function, exp(2πis) is a "monodromy eigenvalue" associated to f. I will formulate a "birational geometric" version of the conjecture, and briefly sketch ongoing work to reduce the conjecture to the case of Newton non-degenerate hypersurfaces. These are hypersurface singularities whose singularities are governed, up to a certain extent, by faces of their Newton polyhedra. The extent to which the former is governed by the latter is a key aspect of the conjecture.