In this thesis, I examine three very different solid-state systems that are all poor conductors when compared to elemental metals. The physics of canonical metals, such as the alkali and noble metals, is well known and is usually idealized in the free-or nearly free-electron picture. Their electron band structures are characterized by parabolic-like bands that cross the Fermi energy and possibly d-bands with flatter dispersions a few eV away. These well-behaved systems lend themselves to the use of simple analytic relations. Each of the three systems that I examine here differs significantly from the nearly-free parabolic band-picture of the electronic structure and require more complex analyses. In the first system of quasicrystals and approximants, we will discover that the electrons are undergoing anomalous diffusion depending on the size and symmetry of the lattices. Of course, as is well known, the details of these atomic lattice are what determine the nature of electronic band structures and how electrons may propagate in solids. In the second system, I find great agreement between my NbAs measurements and calculations on the closely related NbP compound. Incidental to this, I find that a reading of band structures shows that claims of measuring the linear band dispersion in Weyl/Dirac semimetals are not supported by the experimental and theoretical band structures. Finally, in the metallic regime of Nd_(1−x)TiO_3, we find that the Fermi liquid b coefficient is not within the bounds allowed by present models in samples with x = 0.2 and x = 0.15. It is suggested that the approximations used in current models may be why theory and experiment disagree. / Thesis / Doctor of Philosophy (PhD)