An electron moving through a crystal ceases to be a featureless point particle and acquires structure within the unit cell, with far-reaching consequences.In insulators, these include the existence of topological phases with quantized transport properties. The same concepts have turned out to be useful in understanding metals, including two newly discovered classes of three-dimensional materials (Weyl and Dirac semimetals) that generalize the famous massless electronic structure of graphene. We discuss how some long-standing observations of optical properties may actually have a topological origin, which would explain some mysterious properties of the optical activity of quartz. The last part of the talk explains how a classic piece of physics in metals, "the orthogonality catastrophe" that determines the absorption spectrum of X-rays, becomes modified in the presence of topological excitations.