Low Drop Out (LDO) voltage regulators are commonly used to supply low-voltage digital circuits such as microprocessor cores. These digital circuits normally are continuously changing from one mode of operation to another. Therefore, the load demand can change rapidly resulting in large voltage transients at the output of the regulator which can adversely affect the digital circuitry. In this Master's Thesis, design topologies and challenges of very low-power fully integrated On-Chip Low-Dropout (LDO) regulators have been analyzed. Instead of conventional LDO which makes use of a large external capacitor to have better dynamic response and stability, a CapacitorLess LDO (CL-LDO) is chosen on considerations of smaller area. The most challenging part of designing this kind of regulator is achieving high current efficiency by reducing the quiescent current while ensuring good stability response as well as good regulation performance. Thus, different circuit techniques must be carefully added in order to balance the lack of the large external capacitor having the minimum impact on system efficiency. This work focuses on designing a fully integrated low-dropout regulator with good dynamic performance, high regulation performance and ultra-low power consumption. The stability is achieved by the use of two pole-splitting techniques, namely Cascode and Nested-Miller compensation. The good dynamic response with low quiescent current are achieved by the use of an adaptive biasing circuit, a gm-boost circuit and adaptive power transistor architecture.