Prior to the interstate highway system American highways tended to just be roadways that happened to connect together in a route. You can still see these sorts of old style highways all over the place but they are a much different character than modern interstates. On an interstate there are on ramps and off ramps, and the roadway is otherwise completely separated from "surface street" traffic. On older highways the highway would just be a major road that other roads fed into, with a higher speed limit and perhaps more lanes.

In the case of Route 66 it stopped being maintained as a US numbered highway in the 1980s, since interstates made the route effectively obsolete. There are still many other US numbered highways which continue to be maintained throughout the country. Some portions of US 66 still exist as state routes, sometimes as a state route 66, sometimes as a state route by another number, though usually these do not span the entire length that the US route 66 did in those states. Route 66 in Texas and much of New Mexico was upgraded in place to become part of Interstate 40. Other portions of the route are not maintained at all.

Some sections of the route have been revitalized as a "historic route 66". As far as I'm aware there wasn't a significant movement to preserve route 66 until after it had stopped being part of the US highway system, though preservation groups sprouted up fairly quickly afterward (especially "route 66 associations").