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A modern system-on-chip (SoC) integrates a range of analog, digital, and mixed-signal building blocks, each with a dedicated voltage domain to maximize energy efficiency. On-chip low-drop-out regulators (LDOs) are widely used to implement these voltage domains due to their advantages of high power density and the ease of integration to a complementary metal-oxide-semiconductor (CMOS) process. Recently, digital LDOs have gained large attention for their low input voltage support for emerging sub-mW SoCs, portability across designs, and process scalability. However, some of the major drawbacks of a conventional digital LDO design are (i) the trade-off between control loop latency and power dissipation which demands a large output capacitor, (ii) failure to address the performance degradations caused by the parasitics in a practical power grid, and (iii) insufficient power-supply-rejection-ratio (PSRR) and large ripple in the output voltage. Chapters 2 through 4 of this thesis present my research on the design and circuit techniques for improving the aforementioned challenges in fully-integrated digital LDOs. The first work implements a hybrid event- and time-driven control in the digital LDO architecture to improve the response and settling time-related metrics over the existing designs. The second work presents a power delivery system consisting of 9 distributed event-driven digital LDOs for supporting a spatially large digital load. The proposed distributed LDO design achieves large improvements in the steady-state and non-steady-state performances compared to a single LDO design. In the third work, we prototype a digital LDO based on new current-source power-FETs to achieve a high PSRR and low output voltage ripple. Lastly, on-chip voltage regulators have recently found usefulness in hardware security applications. An on-chip LDO can be used to improve the side-channel attack (SCA) resistance of a cryptographic core with design modifications to the classical LDO architecture. However, the existing designs incur non-negligible overheads in performance, power, and silicon area due to the conventional active-for-all-encryption-rounds architecture. In the last chapter, we propose a detection-driven activation technique to achieve a near-zero energy-delay-product (EDP) overhead in a SCA resilient digital LDO. In this architecture, the LDO can detect an attack attempt and enable SCA protection only if an attack is detected.