Here is an image of a kiva at Chaco Canyon (in the U.S. Southwest).  Last class we studied these a bit and although I'm not that big on Ancestral Pueblan architecture it was somewhat interesting, especially since I did not realize such civilizations were so advanced and right in our own backyard.  I believe the Chaco Canyon settlement may have been the one that was abandoned in the 13th century due to a 25-year drought at the time.  The kivas were round, often times subterranean structures used for ritualistic purposes.  They would vary greatly in size, but they all seemed to contain four blocks at the base upon which posts would be placed to help support a wooden roof.  The larger ones seemed to use more complex masonry, and I believe the stones used to anchor the walls were finished off with some sort of mud-crushed stone composite (now washed away) to provide smoothing. These kivas are apparently found at sites of different tribal groups, such as the Hopi and Anasazi.  The precise function of them is uncertain and modern-day Native Americans aren't talking with too much specificity; it was in the 1960s that the Hopi stopped talking to anthropologists.  However, it's not entirely certain that even they would even know since some of these older settlements were abandoned, leaving us (and the Native Americans) with a seemingly broken chain of knowledge.(public domain image of Chaco Canyon kiva)