The accurate measurement of high voltages and currents is vital to monitoring power flows in electric power systems, metering electric power and energy, and, of course, to characterizing the behavior of electrical insulation. NIST has been making precision electrical measurements since its inception a century ago. This paper discusses metrology that is now used or under development at NIST for ac and pulse high voltages and currents. The compensated current comparator is at the heart of most precision ac measurements made at NIST because it offers the greatest sensitivity and lowest measurement uncertainty even today, some forty years after its development. It is used for characterizing ac high voltage and current transformers in terms of their ratio and phase angles, and also for capacitor ratio measurements. Precision ac high voltage dividers with active electronic compensation have also been recently developed. Measurement systems utilizing the magneteoptic Faraday effect are now being developed for both ac and pulsed currents. The basic principles of these devices and systems, their practical limitations, and measurement uncertainties are discussed in this paper.