Pre-Columbian civilizations refers to American indigenous cultures before the European conquests starting in the sixteenth century. Usually it means Middle and South American peoples. For the inside story on the most famous gods, see Aztec Mythology.
Popular perception tends to lump these people together and gets rather tabloid and inventive — see Mayincatec for the trope. In Real Life, the Mayas, Incas, and Aztecs were three very distinct groups.
The Maya are perhaps best remembered for their calendar system, which purportedly predicted the end of the world in 2012. The Long Count system, which divided history into b'ak'tuns of around 395 years each, was used mostly to record history; a shorter 52-year cycle was also used for more human-scale history. 21 December 2012 was simply the start of a new b'ak'tun: not Mayan Doomsday so much as Mayan Y2K. It was the start of the 13th b'ak'tun, which admittedly is supposed to be the final phase of the cycle, but certain inscriptions imply the Mayans did not believe the end of the world would be 2012, and zero inscriptions imply that they did. (Present-day Mayans were, in the months preceding December 2012, similarly underwhelmed by the coming end of the b'ak'tun, not to mention nonplussed that people had felt free to invent a doomsday and attribute it to them.) In the end, Mayan Y2K came and went with (fittingly enough) the same sense of anticlimax that was the hallmark of Regular Y2K.
Around the year 900, classical Mayan civilization went into steep decline. Historians can't quite figure out why. Maybe their governing system collapsed, or maybe there was a famine, or maybe there was some kind of disease or something. By the time of the Spanish invasion, Mayan civilization still existed on a complex level organized into several kingdoms, confederations, and city-states (much like Italy at the time). However, by this time, the trend of Pan-Mesoamericanism (Mesoamerican cultures were becoming similar across the board due to increased trade and communication) had caused their culture to shift dramatically. Their states lasted centuries longer than any other Mesoamerican civilization into the 17th century, probably due to their decentralized structure. Their descendants live in Mexico and Guatemala, but their civilization has died out and their cities are abandoned.
Much like the Greeks, ethnic Mayans retain their languages and culture on a small scale; some Mayan temple sites are still venerated by individual Mayan villages in syncretistic fashion (see Inca, below) and the often-bloody tension between Mayans, Hispanic and Mestizo culture which came down from the north has never really gone away.
By the way, despite their portrayal in the film Apocalypto, the Mayans didn't sacrifice as many people as the Aztecs—though that, admittedly, is a pretty low bar. They preferred to sacrifice captured royals and prisoners for the most part, which naturally led to a lot of wars. However, the Mayans were also very concerned with hygiene, and purification rituals mostly centered around self-sacrifice, usually by means of drawing a barbed thread through the tongue or the penis. Nor were they ignorant of climate or astronomy; their calendar was especially good at predicting eclipses and they also were able to precisely measure the orbits of planets. The Mayan Ballgame was an especially difficult combination of Basketball, Lacrosse, and Rollerball wherein either the captain of the winning team or the losing team got sacrificed; we're not sure which. This was apparently more in line with Gladiator Games, however.
Now we've shooed the elephant out of the room, we can talk about the stuff people usually don't know about the Aztecs. Let's start with history. The Mexica (pronounced "Mesheeka"), a tribe of Nahua people, migrated to central Mexico in the 13th century, from a place somewhere north they called Aztlan, and settled there, soon founding the city-state of Tenochtitlan. Some time after, they allied with two other Nahua city-states, Texcoco and Tlacopan, creating together the Aztec Triple Alliance, better known as the Aztec Empire, in 1428. The Aztecs had a different way of looking at an empire; rather than seeing the lowest parts as something to be ruled from the top, they considered the top to be constituted of the parts. (No, that doesn't mean you get a room in the palace. Get back in the field and keep constituting.) They fell apart around 100 years later, with the Conquistadors allying themselves with the Aztecs' nemesis the Tlaxcala Confederacy and soundly defeating them and destroying the capital.
The word Aztec means "people from Aztlan", where all Nahua tribes that populated the Valley of Mexico originally came from. These groups were very similar to each other and shared language, customs and beliefs. It should be understood though, that usually, when people talk about the Aztecs and the Aztec Empire, they refer to the Mexica and the city of Tenochtitlan, who had superiority over their Acolhua (Texcoco) and Tepanec (Tlacopan) allies. The "Empire" consisted of their two allied/minion city-states and the numerous tributary states, which they would leave to their own business as long as they paid the tribute asked. And the Aztecs threatened to torch any city that violated the agreement to pay tribute. This happened frequently. Hence the sacrifices.
The Aztecs had a heavily agrarian society, with several rather successful farming methods used, and were also one of the first civilizations to implement mandatory education for all children (although, strange to say, they had no true writing system; however, it's highly likely that their system of pictograms and ideograms—which are generally understood to be a kind of proto-writing—would have become a true logographic script if not for the unfortunate incident with the Spaniards). Their stratified society allowed for some social climbing, but the noble-commoner distinction was often difficult to cross. A commoner could be awarded a noble title, usually for taking a certain number of captives in battle, but he could not personally benefit from it. His children, however, would be considered true nobles and receive all the benefits after his death. Commoners were allowed their own land and possessions, however, and were often quite active in the marketplace.
The other main part of Aztec society was warfare. Some of their gods required an enemy to be sacrificed in the temple, so they had to have wars a lot. Sometimes they had Flower Wars, which were ritualistic "mock" wars fought for the purpose of obtaining captives for sacrifices, and also served to train new soldiers. In any case, every male commoner was given basic military training, and noble children were trained more thoroughly. A commoner could take a prisoner for sacrifice in order to become a professional warrior, which was a useful means of social climbing. The Aztecs ruled effectively by having a massive population of which nearly all males could be mobilized in the event of war. The Aztecs also tended to be victorious as there were no need for siege weapons at the time. Mesoamericans were effectively limited to Zerg Rush tactics in the event of a siege. This is why the Aztecs, who had a massive population, nearly always won.
Which is not to say that warfare was unsophisticated. On the contrary, the Aztecs had highly ritualized war preparations, which included, among other things, a sixty-day warning (three months, by the Mesoamerican calendar), and the presentation of a number of weapons to the would-be enemy state, the entire intention being, more-or-less explicitly, to say "we are giving you the fairest fight possible, and we're still going to beat you". Generally, if a city-state acquiesced to the Aztecs' demands, the war would be called off. Even warfare itself was somewhat ritualized, as the primary "goal" of the war was to reach the enemy state's central temple and extinguish the flame therein, proving Huitzilopochtli greater than whoever the local top god was, at which point the enemy (who note, at this point was basically completely occupied by Aztec warriors) was given another chance to surrender. The goal was to take vassal states and sacrifices, not to wipe out the enemy. Despite this, the Aztec were not above underhanded tactics, and greatly valued both their spies, who posed as (and often served as) traders, and a clever strategy (such as invading a cliff-side city via the back by scaling the cliffs).
In 1519 one Hernan Cortes landed with some horses and a few hundred Spanish conquistadors, armed with guns, cannons, and steel swords. Through a combination of terror tactics and shrewd alliances with the Aztecs' many enemies, he gained enough strength to march on Tenochtitlan. His forces were greeted in the city of 200,000 by Aztec leader Moctezuma II himself. A few days later, Cortes took Moctezuma prisoner in his own palace. They remained in the city as "guests" for quite some time, but relations got increasingly tense. When some conquistadors killed most of the Aztec nobility during a festivity, the Aztecs decided they were having none of it. They chose a new leader and drove the Spanish and their allies out of the city. Cortes, undeterred, regrouped, gathered an army of native allies, and went back to besiege Tenochtitlan, which by this time had been weakened by an epidemic of smallpox, which claimed almost half the city population and the new Huey Tlatoani (emperor), Cuitláhuac (pronounced coo-ee-TLA-oo-ac).
A few short months later, nothing would remain of the Aztec Empire... except for the twin capital cites of Tenochtitlan and Tlatelolco (where the last emperor Cuauhtémoc gave his Final Battle), and the name of the future country, and a few of the festival days; and the canals, which were turned into boulevards, and the stones of the temples and palaces, which were recycled into... er, cathedrals and government buildings. However, most of the regional towns were rebuilt in the Spanish style. Today, the Zocalo in Mexico City marks the site of the great plaza of Tenochtitlan; a few original sculptures can be seen in the foundation stones.
A few Spaniards wanted to keep the pyramids and turn them into churches, what with the view and all, but most of them were literally plastered with blood and gore, so only the long-abandoned ones remain. To be fair, the Spaniards were no pikers note : entire tribes would be slaughtered under the policy of "convert or die"; and given the apparent collapse of the Aztecs, who were already the bane of other tribes in the region, they had no want of willing converts.
The Aztec language, Nahuatl, is still spoken today; it still flavors the Spanish in much of Mexico and has given the world some fairly useful words like tomato (from xitomatl), chilli (from chīlli), chocolate (from xocolātl), and coyote (from cóyotl). The image associated with the myth of the founding of Tenochtitlan, an eagle devouring a snake on a cactus, is today depicted in the Coat of Arms of Mexico and on the Mexican flag.
Entrance to the nobility was based on merit as determined by some sort of Inca SAT-equivalent. They were very bureaucracy- and business-oriented, as they pretty much had to be to rule an empire that large. Even their marriages were strictly a business deal. The Incas believed in equality, that All Men Must Work In Order To Live, and every citizen — even nobility — paid tribute in the form of some manual labor as a public service.
They built a highway system and remarkably stable stone structures, given the unstable geology of the region — possibly due to their propensity to build things out of ginormous stone blocks carved to exacting specifications. Much of the imperial capital of Cuzco is still standing and in use today, along with thousands of terraces and granaries. They used these to take advantage of the region's unique climate that allowed them to grow different crops at different elevations throughout the Andes, and export them only a short distance to market, so that Imperial runners could bring fresh fish to Cuzco every day, along with mail, despite the lack of a wheelnote or written languagenote .
Moreso than any other culture in the region, the Inca chose to survive and adapt to Spanish conquest, with the last Inca Emperor instructing his citizens to convert to Christianity and worship Inca traditions on the side, which some Quechua people continue to do today. Their language and much of their agrarian lifestyle has also survived. They were aided in this by the mountainous nature of the region which left the Spaniards dependent on Inca infrastructure and foodstuffs, a fact which protected the Inca from wholesale slaughter. In particular, Incan roads inhibited Spanish spread. European mountain roads consist of multiple switchbacks in order to accommodate the proclivities of the Eurasian horse. In contrast, Incan roads were built with the llama and alpaca in mind, and consist of stairsteps up the sides of mountains. Eurasian horses hated them.
The Inca system of manual labor as a public service, paid for in coca leaf, also survives in Peru.note It helps that Inca beliefs were a little easier to reconcile with European values than, say, the Aztecs'.
Egalitarian tribes grew and evolved into chiefdoms with social stratification. This enabled increased food production (through specialization and centralized food storage), which fueled greater population growth, which led to greater social stratification and more complex societies and political structures.
At their height, the mound culture built the earthen mounds for which they are named. Their architecture was then built on top of those mounds. They didn't work in stone or metal, hence little is known about them as very few of their artifacts or architecture have survived. However, it is known that the mound culture did spread throughout much of central and eastern North America, and it is suspected to have developed to the point where one mound city was capable of exerting political influence or authority nearby cities.
Eastern mound culture was the first to encounter Europeans, and proceeded as is described in most Eagle Land textbooks. The interactions were occasionally violent, occasionally peaceful, but inevitably ended poorly for the natives thanks to European diseases and weaponry among other things. Mound cultures in the central valley probably never had the opportunity to meet Europeans, as diseases spread through the interior of the continent much faster than the Europeans themselves. Measles and smallpox decimated and scattered the mound builders and, denuded of elders (repositories of knowledge) and necessary population, the nascent cities, city-states, and proto-empires collapsed. Some populations (such as the Cherokee) retained enough population and continuity to link themselves to the mounds their ancestors had built through oral tradition. Others were unaware that the mounds they lived beside had been built by human beings, let alone by their ancestors.
There are also two closely related but less famous cultures, the Mogollon (pronounced moh-ghi-yohn)and the Hohokam. All three cultures seem to have had some contact with Mesoamerica, as chocolate and macaw feathers can be found at archaeological sites. One Hohokam settlement even had a ball court, presumably for the same sort of game the Aztecs and Maya played.
One puebloan motif that most Americans can recognize is the fertility god Kokopelli. They are also sometimes associated with Conspiracy Theories, possibly because in many people's minds they are in the same general area as Roswell and Area 51.
And then again, there are these giant stone balls in Costa Rica.
Goodbye -- 'til next time.