US airlines (minus Southwest) still use SABRE for reservation and flight management. A system developed for DARPA in the 50s. Basically everything is run in virtual machines I believe, but there are probably still some SABRE terminals out there.

Getting that system back up and running will be a nightmare as it's integrated into basically every reservation service on the planet. That's probably why they want all flights grounded because anything that happens while the system is down will have to be added manually later.