Noise coupling on the power distribution networks (PDN) or between PDN and signal traces is becoming one of the main challenges in designing above GHz high-speed digital circuits. Developing an efficient and accurate modeling method is essential to understand the noise coupling mechanism and then solve the problem afterwards. In addition, development of new noise mitigation technology is also important for future high-speed circuit systems. In this invited paper, a novel modeling methodology that is based on the physics-based equivalent circuit model will be introduced, and an example of multiple layer PCB circuits will be modeled and validated with good accuracy. Based on the periodic structure concept, several new electromagnetic bandgap structures (EBG), such as coplanar EBG, photonic crystal power layer (PCPL), and ground surface perturbation lattice (GSPL), will be introduced for the mitigation of power/ground noise. The trade/offs of all these structures will be discussed.