Currently, we are in an era of neutrino physics in which neutrino oscillation experiments are focusing on doing precision measurements. In this dissertation, we investigate what is important to consider when doing these precise experiments, especially in light of significant unresolved anomalies. We look at four general categories of considerations: systematic uncertainties, fundamental assumptions, parameterization-dependence of interpretations, and Beyond the Standard Model (BSM) scenarios. By performing a simulation using GLoBES, we find that uncertainties in the fine structure of the reactor neutrino spectrum could be vitally important to JUNO, a reactor neutrino experiment being built in China, so a reference spectrum with comparable energy resolution to JUNO is needed in order to alleviate this uncertainty. In addition, we determine that with their fix of the fine structure problem, JUNO can test the existence of a quantum interference term in the oscillation probability. We also reason that the CP-violating phase is very parameterization dependent, and the Jarlskog invariant is better for talking about amounts of CP violation in neutrino oscillations. Finally, we discover that CP-violating neutrino Non-Standard Interactions (NSIs) could already be affecting the outcomes of T2K and NOνA, two accelerator neutrino experiments, and may be why there is a tension in these two data sets. / Doctor of Philosophy / Neutrinos are very weakly interacting, fundamental particles that are extremely plentiful in the universe. There are three known types (or flavors) of neutrinos, and the fact that they change flavors (or oscillate) informs us that their mass is not zero, but no experiments have been able to put a lower bound on the smallest neutrino mass. Now that experiments measuring neutrino oscillations have become more precise and some significant anomalies remain unresolved, there are considerations that have become important to investigate. In this paper, we look at four of these considerations: • Uncertainties in the finer shapes in the energy spectrum of neutrinos coming from a nuclear reactor (Chapter 2): We find that these uncertainties could destroy the ability of the Jiangmen Underground Neutrino Observatory (JUNO) to meet one of its major goals, unless they measured the spectrum at a spot close to the reactor with a really good energy resolution (comparable to that of JUNO). • An assumption about quantum mechanics being the foundation of particles and their interactions (Chapter 3): We determine that by heeding our warning in Chapter 2, JUNO will be able to test the existence of the term in the oscillation probability arising out of quantum interference. • How the neutrino oscillation parameter known as the CP-violating phase is dependent on the parameterization scheme used for the matrix describing how the flavors mix to make neutrino oscillation possible (Chapter 4): We find that the parameterization dependence is drastic, and if we want to discuss how much CP violation (i.e. a measure of how neutrinos behave differently from their anti-matter counterparts) exists in neutrino oscillations, we should talk about a quantity called the Jarlskog invariant. • The possibility of interactions existing between neutrinos and other particles that are not part of the Standard Model of Particle Physics, i.e. neutrino Non-Standard Interactions (NSIs) (Chapter 5): We discover that NSIs that are CP-violating can actually explain a current discrepancy between two neutrino oscillation experiments: Tokai to Kamioka Nuclear Decay Experiment (T2K) and NuMI Off-axis ν e Appearance (NOνA).