Required Navigation Performance (RNP) procedures to parallel runways that include curved approaches offer many benefits to the flying public, airlines, and nearby residents on the ground. Fewer track miles are required during approach, thus enabling decreases in missed connections, fuel burn, emissions, and noise footprint. This paper documents research on independent and dependent RNP approaches to parallel runways. The goals are to provide recommendations to support the International Civil Aviation Organization (ICAO) rule changes and to promote the growth of these RNP-enabled procedures around the world.The paper will be structured as follows: After pointing out the benefits that curved RNP procedures provide at parallel runway environments, we will summarize and compare current ICAO and Federal Aviation Administration (FAA) rules for simultaneous approach operations as well as proposed revisions of ICAO's guidelines. We conclude that current ICAO standards and their proposed revisions will not fully reflect the changes needed to achieve all of the benefits that curved RNP procedures can provide in parallel runway environments. Accordingly, we will identify areas within the guidelines that need to be extended for this purpose.We will then describe two methodologies to enable safe RNP procedures to parallel runways that include curved approaches. Those two methodologies are based on safety concepts that were developed for RNP-established procedures at Seattle and safety concepts developed for Frankfurt Airport. Finally, we will conclude with possible ways to extend ICAO's guidelines based on these concepts and identify further aspects that need to be considered, such as the potential of nuisance Airborne Collision Avoidance System (ACAS) alerts.