The Anasazi became the Hopi and other Puebloan peoples - "Anasazi" (a Navajo word meaning, roughly, "ancestors of our enemies") is being phased out in most literature in favor of Ancestral Puebloan. The Hopi in particular have never really doubted their connection to what archaeologists call the Sinagua people. However, this wasn't confirmed to archaeology until the discovery of the "Magician's Burial" in 1939. There, a grave was found with over 600 objects, which was unusual since most graves might have 8-12. A number of these objects were identified as ceremonial by Hopi members of the expedition, and different individuals identified objects independently. A few Hopi were even shown only part of the collection, and were then able to identify what else should have been (and unbeknownst to them, in fact were) found with them. There are also petroglyphs at Mesa Verde and other sites showing women wearing the distinctive Hopi hair bun. It's important to keep in mind that labels like "Anasazi" and "Sinagua" are modern constructs; we may be assigning political/ethnic distinctions where none actually existed.

The sites at Mesa Verde are pretty well hidden, but local Utes knew about them before their "discovery" in the 1870s, and Navajos had been familiar with Chaco Canyon since descending from Canada probably around the 13th or 14th century. Both Utes and Navajos viewed these sites as sacred remnants of a past culture, and thought that the buildings' abandonment was a bad sign for the type of close, sedentary living they implied. They avoided the areas, and especially did not live in them. However, Navajos did use Ancestral Puebloan hand-and-toeholds, and likely AP-utilized or -improved caves in Canyon de Chelly, during wars against Spanish, Mexican, and American armies and raiding parties.

Sources: John C. McGregor, "Burial of an Early American Magician"; Hampton Sides, Blood and Thunder; a season working at Mesa Verde.