The objective of this dissertation is to derive a set of compact physical models addressing power integrity issues in high performance gigascale integration (GSI) systems and three-dimensional (3-D) systems. The aggressive scaling of CMOS integrated circuits makes the design of power distribution networks a serious challenge. This is because the supply current and clock frequency are increasing, which increases the power supply noise. The scaling of the supply voltage slowed down in recent years, but the logic on the integrated circuit (IC) still becomes more sensitive to any supply voltage change because of the decreasing clock cycle and therefore noise margin. Excessive power supply noise can lead to severe degradation of chip performance and even logic failure. Therefore, power supply noise modeling and power integrity validation are of great significance in GSI systems and 3-D systems. Compact physical models enable quick recognition of the power supply noise without doing dedicated simulations. In this dissertation, accurate and compact physical models for the power supply noise are derived for power hungry blocks, hot spots, 3-D chip stacks, and chip/package co-design. The impacts of noise on transmission line performance are also investigated using compact physical modeling schemes. The models can help designers gain sufficient physical insights into the complicated power delivery system and tradeoff various important chip and package design parameters during the early stages of design. The models are compared with commercial tools and display high accuracy.