Angle-resolved photoemission spectroscopy (ARPES) is one of the most direct and powerful probes for studying the physics of solids. ARPES takes a \u22snapshot\u22 of electrons in momentum space (k-space) to reveal details of the dispersion relation E(k), as well as information about the lifetimes of interacting quasiparticles. From this we learn not only where the electrons live, but also, if we are crafty, what they are doing. Beginning with work by our group in 2006 using a 6-eV laser, ARPES experiments have begun to make use of a new, low photon energy regime (roughly hν = 6-9 eV). These low photon energies give drastic improvements in momentum resolution, photoelectron escape depths, and overall spectral sharpness. This has led to several important new findings in the intensively-studied problem of high-temperature superconductivity. This thesis will focus on two of the latest results from our group using low-energy ARPES (LE-ARPES) to study the cuprate high-Tc superconductor Bi2Sr2CaCu2O8+δ (Bi2212). The first of these is an investigation into the nature of many-body interactions at a well-known energy scale (~60-70 meV) where the dispersion shows a large bend, or \u22kink\u22. Using LE-ARPES measurements, the k-dependence of this kink is investigated in unprecedented detail. An attempt is then made to map the feature\u27s k evolution into the scattering q-space of boson dispersions. In our analysis, the q-dispersion of the kink bears more resemblance to dispersive spin excitations than phonons -- a surprising finding in light of previous evidence that the the kink originates from interactions with phonons. However, phonons cannot be ruled out, and the results may hint that both types of interactions contribute to the main nodal kink. A second result is the discovery of a new ultralow (\u3c 10 meV) energy scale for electron interactions, corresponding to a distinct, smaller kink in the electron dispersion. The temperature and doping dependence of this feature show not only that it turns on near Tc -- signalling a possible relation to the mechanism of high-Tc superconductivity -- but also that it leads to a subtle breakdown of the so-called \u22universal\u22 Fermi velocity vF along nodes of the anisotropic superconducting gap. Moreover, vF is found to depend quite strongly on temperature, which may be an important factor in the physics of cuprates
