Next generation microprocessor (Vcore) requirements for high current slew rates and fast transient response together with low output voltage have posed great challenges on voltage regulator (VR) design . Since the debut of Intel 80X86 series, CPUs have greatly improved in performance with a dramatic increase on power consumption. According to the latest Intel VR11 design guidelines , the operational current may ramp up to 140A with typical voltages in the 1.1V to 1.4V range, while the slew rate of the transient current can be as high as 1.9A/ns [1, 2]. Meanwhile, the transient-response requirements are becoming stringer and stringer. This dissertation presents several topics on how to improve transient response for multi-phase voltage regulators. The Adaptive Modulation Control (AMC) is a type of non-linear control method which has proven to be effective in achieving high bandwidth designs as well as stabilizing the control loop during large load transients. It adaptively adjusts control bandwidth by changing the modulation gain, depending on different load conditions. With the AMC, a multiphase voltage regulator can be designed with an aggressively high bandwidth. When in heavy load transients where the loop could be potentially unstable, the bandwidth is lowered. Therefore, the AMC provides an optimal means for robust high-bandwidth design with excellent transient performance. The Error Amplifier Voltage Positioning (EAVP) is proposed to improve transient response by removing undesired spikes and dips after initial transient response. The EAVP works only in a short period of time during transient events without modifying the power stage and changing the control loop gain. It facilitates the error amplifier voltage recovering during transient events, achieving a fast settling time without impact on the whole control loop. Coupled inductors are an emerging topology for computing power supplies as VRs with coupled inductors show dynamic and steady-state advantages over traditional VRs. This dissertation first covers the coupling mechanism in terms of both electrical and reluctance modeling. Since the magnetizing inductance plays an important role in the coupled-inductor operation, a unified State-Space Averaging model is then built for a two-phase coupled-inductor voltage regulator. The DC solutions of the phase currents are derived in order to show the impact of the magnetizing inductance on phase current balancing. A small signal model is obtained based on the state-space-averaging model. The effects of magnetizing inductance on dynamic performance are presented. The limitations of conventional DCR current-sensing for coupled inductors are addressed. Traditional inductor DCR current sensing topology and prior arts fail to extract phase currents for coupled inductors. Two new DCR current sensing topologies for coupled inductors are presented in this dissertation. By implementation of simple RC networks, the proposed topologies can preserve the coupling effect between phases. As a result, accurate phase inductor currents and total current can be sensed, resulting in excellent current and voltage regulation. While coupled-inductor topologies are showing advantages in transient response and are becoming industry practices, they are suffering from low steady-state operating efficiency. Motivated by the challenging transient and efficiency requirements, this dissertation proposes a Full Bridge Coupled Inductor (FBCI) scheme which is able to improve transient response as well as savor high efficiency at (a) steady state. The FBCI can change the circuit configuration under different operational conditions. Its "flexible" topology is able to optimize both transient response and steady-state efficiency. The flexible core configuration makes implementation easy and clear of IP issues. A novel design methodology for planar magnetics based on numerical analysis of electromagnetic fields is offered and successfully applied to the design of low-voltage high power density dc-dc converters. The design methodology features intense use of FEM simulation. The design issues of planar magnetics, including loss mechanism in copper and core, winding design on PCB, core selections, winding arrangements and so on are first reviewed. After that, FEM simulators are introduced to numerically compute the core loss and winding loss. Consequently, a software platform for magnetics design is established, and optimized magnetics can then be achieved. Dynamic voltage scaling (DVS) technology is a common industry practice in optimizing power consumption of microprocessors by dynamically altering the supply voltage under different operational modes, while maintaining the performance requirements. During DVS operation, it is desirable to position the output voltage to a new level commanded by the microprocessor (CPU) with minimum delay. However, voltage deviation and slow settling time usually exist due to large output capacitance and compensation delay in voltage regulators. Although optimal DVS can be achieved by modifying the output capacitance and compensation, this method is limited by constraints from stringent static and dynamic requirements. In this dissertation, the effects of output capacitance and compensation network on DVS operation are discussed in detail. An active compensator scheme is then proposed to ensure smooth transition of the output voltage without change of power stage and compensation during DVS. Simulation and experimental results are included to demonstrate the effectiveness of the proposed scheme.