Abstract: We discuss the so-called “matching functions” technique, recently formulated by Gogolev and Rodriguez-Hertz to prove rigidity results for expanding maps, codimension one Anosov diffeomorphisms, and codimension Anosov flows. We compare this to the classical method of “matching measures” first introduced by de la Llave, to prove rigidity results for surface Anosov diffeomorphisms with matching periodic data.