Based on the information available, the current status of the trains running today can be found on various platforms such as SubwayStats.com, the official Twitter account of NYCT Subway, the MTA website, MTA Train Status website, and Downdetector. These platforms provide real-time updates on the status, delays, and closures for each train, as well as any service changes or disruptions. It is recommended to check these sources for the most up-to-date information on the trains running today.