It is only now becoming clear that scanning tunneling microscopy and spectroscopy serve a vital purpose in probing not only the electronic structure of quantum mechanical states in real space, but also in momentum space. In studies of the underdoped high-$T_C$ cuprate superconductors, spectroscopy reveals two energetic gap-like features. The investigations described in this dissertation reveal that the higher energy spectral feature contributes to a disordered glass of electronic domains. These objects break long-range translational and rotational symmetry, but are nevertheless ordered on the atomic scale, consisting internally of bond-centered Cu-O-Cu objects. Such features were discovered in two lightly hole-doped cuprate compounds, $Bi_{2}Sr_{2}Dy_{x}Ca_{1-x}Cu_{2}O_{8+\delta}$ and $Ca_{2-x}Na_{x}CuO_{2}Cl_{2}$, which share no common lattice chemistry except for at least one $CuO_2$ plane. Furthermore, it is possible to utilize Bogoliubov quasiparticle interference to probe the spectral weight of cuprate samples in $\vec{k}$-space. These calculations produce the so-called "bananas", or Fermi arcs, at low ($\sim$6-30mV) energies. The octet model of quasiparticle scattering analysis reveals energetic dispersion which increases in intensity as doping is decreased from optimal percentages. In addition, fits to a model for the angular dependence of a d-wave order parameter suggest a relationship between the higher-energy gap and the model parameters found via quasiparticle interference. Disappearance of quasiparticle intensity occurs quite near a $\sqrt{2}\times\sqrt{2}$ zone boundary, a curious observation considering that the samples studied are not antiferromagnets per se. Since low-energy Bogoliubov states are well-defined in $\vec{k}$-space and the higher-energy electronic domain glass states are well-defined in $\vec{r}$-space, an energetic phase separation of two types of quantum eigenstate are proposed. Further, the growth of spectral gaps from the optimally doped to the underdoped regimes suggests that the disordered patterns of the electronic domain glass measured via tunneling asymmetry studies are actually real-space measurements of the electronic excitations within the pseudogap regime. This picture eludes to a d-wave superconductor which, with falling doping, relents its superconducting order to quasiparticle scattering within the pseudogap domain, while the pseudogap order splits away and gradually concedes to the antiferromagnetic Mott insulator parent state.