The term "Aztecs" is used in the title of this since that's the word in common usage; everyone "knows" the Aztecs were conquered by Cortez.
The trouble is, this isn't quite correct. None of the inhabitants of Mexico and Central America referred to themselves as "Aztecs;" this word, which probably means "Those Who Came From Aztlan (the place of herons)," encompassed seven tribes who'd migrated from the Northeast several hundred years before the Conquisadors' arrival. The Conquistadors fought with one of these tribes, the one dominant at the time, the Mexica (from which our term "Mexico" is derived). Some others, for example the Tlaxcalans and the Acolhuas of Texcoco, threw their lot in with Cortez, who could not possibly have conquered the Mexica without the thousands of Indian allies who flocked to his side.
All the "Aztec" tribes were just a part of the vast culture of Mesoamerica the Spaniards destroyed. Culturally and technologically, the Tarascans of Michoacan were more advanced than the Mexica; we do not hear of them because smallpox decimated them before Europeans reached them. There were many others, too; the Zapotecs, the Mixtecs, the Huaxtecs, and so on, all of whom contibuted greatly to what we think of as "Aztec" culture.
This culture had an old history in the Americas, too, stretching back to the Olmecs of the Gulf Coast, to the great city of Teotihuacan (the pyramids north of Mexico City, commonly called "Aztec" but actually ancient by the time the tribes from Aztlan arrived), to the Toltecs of Tula. A rich and full culture--plundered and destroyed by Spaniards interested mainly in gold. But many of their monumental structures remain--like the Great Pyramid at Cholula, the largest man-made structure on the planet even today. And their history remains, too, with many valuable lessons for us still...