Providing power quality (PQ) for 21st-century needs is one of the widely accepted principal characteristics of the envisioned Smart Grid because we will have more and more PQ-sensitive loads such as microprocessor-based devices, critical manufacturing processes, and data centers . Our future global competitiveness demands disturbance-free operation of the digital devices that empower the productivity of our economy. It is expected that the Smart Grid will provide a reliable power supply with fewer and briefer outages, cleaner power, and self-healing power systems, through advanced PQ monitoring, analysis of the measurement data, diagnosis of PQ disturbances, identification of the root causes, and timely automated controls. Note that computational intelligence(CI) has been an integral, significant part of advancing and expanding the horizons of this PQ research. The capabilities and applications of CI for PQ are continually evolving due to advanced PQ monitoring (or recording) devices. The objective of this chapter is to present these CI applications such as signal processing and artificial intelligence (AI) techniques to help understand, measure, and mitigate PQ phenomena. This chapter also describes challenges and potential applications in turning raw PQ measurement data to a much more valuable and actionable knowledge in order to improve PQ performance and produce real financial benefits as well.