Researchers have proven that β-Ga2O3 devices can match state of the artSiC power devices. However, further advancement for both higher breakdown voltages and thus higher surface electric fields is needed to entice adoption of β-Ga2O3 power electronics. This dissertation provides a holistic discussion of the material requirementsfor high-field operation of gallium oxide, starting from closed-form descriptions of current transport. We initially provide a review of on-state current mecha- nism to provide a framework of injection-limited and conduction-limited trans- port. We use this to probe the minimum requirements for off-state injection- limited and conduction-limited transport to approach intrinsic breakdown at commercially-comparable reverse leakage current densities. With these minimum requirements guiding anode design, we utilize the col-laborative development of novel low-energy deposition methods such as ozone- MBE and mist-CVD to create highly-uniform and high-quality junctions. In the case of crystalline metal oxides IrO2, RuO2, and PtO, peak surface electric fields exceeding 6 MV/cm are realized with barrier heights nearing and exceeding 2 eV. We further critically assess the predominant p-type material used for Ga2O3 heterojunctions and demonstrate a high-quality one-sided interface for both P- N junctions and anode-connected p-NiO field plates. We further observe from the closed-form mechanisms that compensating de-fects deeper than 1 eV exceed the minimum requirement to approach intrinsic breakdown. We demonstrate, in plain language, the distinction between acti- vating a deep-level dopant and observing resistive behavior. We further show a use case of assessing the presence of shallow defects and if they inhibit resistive behavior in both DC and switching operation.