Gallium Oxide (Ga2O3) is an ultra-wide bandgap semiconductor with a bandgap of 4.5–4.9 eV, which is larger than that of Silicon (Si), Silicon Carbide (SiC), and Gallium Nitride (GaN). A benefit of this ultra-wide bandgap is the high-temperature stability due to the low intrinsic carrier concentration. Another benefit is the high critical electric field (Ec), which is estimated to be from 6 MV/cm to 8 MV/cm in Ga2O3. This allows for a superior Baliga's figure of merit (BFOM) of unipolar Ga2O3 power devices, i.e., they potentially can achieve a smaller specific on-resistance (RON,SP) as compared to the Si, SiC, and GaN devices with the same breakdown voltage (BV). The above prospects make Ga2O3 devices the promising candidates for next-generation power electronics. This dissertation explores the design, fabrication, characterization, and packaging of vertical β-Ga2O3 Schottky barrier diodes (SBDs) and P-N diodes. The power SBDs allow for a small forward voltage and a fast switching speed; thus, it is ubiquitously utilized in power electronics systems. Meanwhile, the Ga2O3 power P-N diodes have the benefit of smaller leakage current, and the diode structure could be a building block for many advanced diodes and transistors. Hence, the study of Ga2O3 Schottky and P-N diodes is expected to provide the foundation for developing a series of Ga2O3 power devices. Firstly, vertical Ga2O3 Schottky and P-N diodes with a novel edge termination (ET), the multi-layer Nickel Oxide (NiO) junction termination extension (JTE), are fabricated on Ga2O3 substrates. This multi-JTE NiO structure decreases the peak electric field (Epeak) at the triple point of device edge when the Ga2O3 diodes are reversely biased. For SBDs, BV reach 2.5 kV, the 1-D junction field reaches 3.08 MV/cm, and the BFOM exceeds 1 GW/cm2. For P-N diodes, BV reaches 3.3 kV, the junction field reaches 4.2 MV/cm, and the BFOM reaches 2.6 GW/cm2. These results are among the highest in Ga2O3 power devices and are comparable to the state-of-the-art vertical GaN Schottky and P-N diodes. Notably, all these diodes are small-area devices. Secondly, large-area (3 mm×3 mm anode size) Ga2O3 Schottky and P-N diodes with high current capability are fabricated to explore the packaging, thermal management, and switching characteristics of Ga2O3 diodes. The same ET is applied for the large-area P-N diode. The fabricated large-area P-N diodes have a turn-on voltage of 2 V, a differential on-resistance (Ron) of 0.2 Ω, and they can reach at least 15 A when measured in the pulse mode. The BV of large-area Ga2O3 P-N diodes varies due to the fabrication non-uniformity, but the best device achieves a BV of 1.6 kV, standing among the highest values reported for large-area Ga2O3 diodes. Also, the large-area Ga2O3 SBDs with similar current rating but with a FP ET are fabricated mainly for the packaging and thermal management studies. Thirdly, medium-area Ga2O3 P-N diodes with a current over 1 A and a higher yield of BV are fabricated to evaluate the JTE's capacitance and switching characteristics. The JTE accounts for only ~11% of the junction capacitance of this 1 A diode, and the percentage is expected to be even smaller for higher-current diodes. The turn-on/off speed and reverse recovery time of the diode are comparable to commercial SiC Schottky barrier diodes under the on-wafer switching test. These results show the viability of NiO JTE for enabling a fast switching speed in high-voltage Ga2O3 power devices. Fourthly, the fabricated large-area Ga2O3 diodes are packaged using silver sintering as the die attach. The sintered silver joint has higher thermal conductivity (kT) and better reliability as compared to the solder joint. Due to the low kT of Ga2O3 material, junction-side-cooled (JSC) packaging configuration is necessary for Ga2O3 devices. For the packaged device, its junction-to-case thermal resistance (RθJC) is measured in the bottom-side-cooled (BSC) and junction-side-cooled (JSC) configuration by the transient dual interface method according to the JEDEC 51-14 standard. The RθJC of the junction- and bottom-cooled Ga2O3 SBD is measured to be 0.5 K/W and 1.43 K/W, respectively. The former RθJC is lower than that of similarly-rated commercial SiC SBDs. This manifests the significance of JSC packaging for the thermal management of Ga2O3 devices. Fifthly, to evaluate the electrothermal robustness of the packaged Ga2O3 devices, the surge current capability of JSC packaged Ga2O3 SBDs are measured. The Ga2O3 SBDs with proper packaging show high surge current capabilities. The double-side-cooled (DSC) large-area Ga2O3 SBDs can sustain a peak surge current over 60 A, with a ratio between the peak surge current and the rated current superior to that of similarly-rated commercial SiC SBDs. These results show the excellent ruggedness of Ga2O3 power devices. Finally, a Ga2O3 integrated diode module consisting of four single-diode sub-modules is designed and fabricated. For many power electronics applications, high current is desired; however, for emerging semiconductors, the current upscaling is difficult by directly increasing the device area because of the limitation of heat extraction capability and the limited material/processing yield. Here we explore the paralleling of multiple Ga2O3 P-N diodes to increase the current level. For each sub-module, the JSC packaging structure is used for heat extraction, and a metal post is sintered to the anode for electric field (E-field) management. RθJC is measured to be 1 W/K for each sub-module. On-board double-pulsed test is performed for both the sub-module and the full module. The sub-module and full module demonstrate 400 V, 10 A and 150 V, 70 A switching capabilities, respectively. This is the first demonstration of Ga2O3 power module and shows a promising approach to upscale of the power level of Ga2O3 power electronics. In addition to Ga2O3 device study, a research is conducted to explore the chip size (Achip) minimization for wide-bandgap (WBG) and ultra-wide bandgap (UWBG) power devices. Achip optimization is particularly critical for WBG and UWBG power devices and modules due to the high material cost. This work presents a new, holistic, electrothermal approach to optimize Achip for a given set of target specifications including BV, conduction current (I0), and switching frequency (f). The conduction and switching losses of the device are considered, as well as the heat dissipation in the chip and its package. For a given BV and I0, the optimal Achip, Wdr, and Ndr show strong dependence on f and thermal management. Our approach offers more accurate cost analysis and design guidelines for power modules. In summary, this dissertation covers the design, fabrication, characterization, and packaging of Ga2O3 Schottky and P-N diodes, with the aim to advance Ga2O3 devices to power electronics applications. This dissertation addresses many knowledge gaps on Ga2O3 devices, including the voltage upscaling (ET), current upscaling (large-area device fabrication, packaging, and thermal management), and their concurrence (module demonstration), as well as the circuit-level switching characterizations.