The constant scaling of supply voltages in state-of-the-art CMOS processes has led to severe limitations for many analog circuit applications. Some CMOS processes have addressed this issue by adding high voltage MOSFETs to their process. Although it can be a completely viable solution, it usually requires a changing of the process flow or adding additional steps, which in turn, leads to an increase in fabrication costs. Si-MESFETs (silicon-metal-semiconductor-field-effect-transistors) from Arizona State University (ASU) on the other hand, have an inherent high voltage capability and can be added to any silicon-on-insulator (SOI) or silicon-on-sapphire (SOS) CMOS process free of cost. This has been proved at five different commercial foundries on technologies ranging from 0.5 to 0.15 μm. Another critical issue facing CMOS processes on insulated substrates is the scaling of the thin silicon channel. Consequently, the future direction of SOI/SOS CMOS transistors may trend away from partially depleted (PD) transistors and towards fully depleted (FD) devices. FD-CMOS are already being implemented in multiple applications due to their very low power capability. Since the FD-CMOS market only figures to grow, it is appropriate that MESFETs also be developed for these processes. The beginning of this thesis will focus on the device aspects of both PD and FD-MESFETs including their layout structure, DC and RF characteristics, and breakdown voltage. The second half will then shift the focus towards implementing both types of MESFETs in an analog circuit application. Aside from their high breakdown ability, MESFETs also feature depletion mode operation, easy to adjust but well controlled threshold voltages, and fT's up to 45 GHz. Those unique characteristics can allow certain designs that were previously difficult to implement or prohibitively expensive using conventional technologies to now be achieved. One such application which benefits is low dropout regulators (LDO). By utilizing an n-channel MESFET as the pass transistor, a LDO featuring very low dropout voltage, fast transient response, and stable operation can be achieved without an external capacitance. With the focus of this thesis being MESFET based LDOs, the device discussion will be mostly tailored towards optimally designing MESFETs for this particular application.