The Mexica
The epicenter of Mesoamerica was the "The Triple Alliance", this was dominated by the ruling tribe, the Mexica (the people from Aztlan- Aztec). Note: They weren't actually the Aztecs.
Also, the peak of Mayan civilization, pre-Classical Maya (2000 BCE - 250 CE) didn't exist during the same time as the "Aztecs", they were politically fragmented and under influence by central Mexico's Teotihuacan city-state during the Classical Period (250-950 CE) and in total disarray by the time the Triple Alliance came around (1335 CE), many of the great Mayan cities were abandoned and groups migrated North and South. Their territory was still inhabited, just not to its original extent. They were a neutral trade power for the Triple Alliance. The Inca Empire (the last of many great Andean Civilizations) was so far south that they probably had little direct contact and more than likely traded indirectly. There's also a possibility of extensive sea trading happening between areas in the Gulf, including trade with tribes further North. Land trade routes may have included northern tribes such as the Anasazi, other uto-Aztecan speaking tribes, and the Cahokia.
The Triple Alliance
When the Mexica first arrived in the Central Valley, perhaps around the collapse of Toltec civilization, it was brimming with populated societies. The Mexica, being weaker outcasts, were cast out to the marshes of Lake Texcoco where they had to build a city on an island- slowly growing in power as hired mercenaries for the existing city-states of the Tepenacah. As they grew, they broke into two groups, the Tenocha and Tlatelolco (perhaps similar to Sparta's relationship with Athens).
The Tlatelolca [people] were a part of the Mexica, a Nahuatl-speaking people
who arrived in what is now central Mexico in the 13th century. The
Mexica settled on an island in Lake Texcoco, founding the altepetl of
Mexico-Tenochtitlan on the southern portion of the island. In 1337, a
group of dissident Mexica broke away from the Tenochca leadership in
Tenochtitlan and founded Mexico-Tlatelolco on the northern portion of
the island. Tenochtitlan was closely tied with its sister city, which
was largely dependent on the market of Tlatelolco, the most important
site of commerce in the area
My buddy David Bowles breaks down the etymology of "The Triple Alliance" in his article, and briefly discusses the formation of the alliance between the Mexica, Tetzcocah, and Tepanec city-states, each holding a geographic location surrounding Lake Texcoco.
But what were those three places? Mēxihco-Tenōchtitlan, Tetzcohco, &
Tlacōpan. The three city-states that united to overthrow the
Tepanēcah.
The "Aztecs" as mistakenly called, are three different city-states that united to overthrow the Tepanecahs (of which the Tlacopan were related). This formed the core of the empire, conquering nearby tribes, creating tributary states (the shaded areas on the map), and taking prisoners for sacrificial offerings.
Breaking down the factions
The Aztec would fight short wars called the "Flower Wars" with nearby city-states (some of these neutral powers), and rather than outright conquering, usually they would fight till they met a quota of tribute set by the Tlatoani (rulers) or their priests. They would attempt to demand tribute in the form of goods, wealth, soldiers, or prisoners for offerings. They were allied with Teotitlan to their Southeast, and fought most often with the Tarascans (Purepecha) west/northwest of them and with the Tlaxcalans to their East. The Chichimeca in the North were nomadic and considered barbarians by the Aztecs, they fought fiercely with them (the Spanish were even defeated during the Chichimeca War). Along the Gulf coast, the Huastec people were a Mayan colony conquered by the Aztecs, with tribute being demanded.
In the South, the Mixtecs mostly rivaled with the Zapotecs in the South, but at times they would also come into conflict with the Aztecs who sought tribute. The Tlapanec, or Yopi as they were called by the Aztecs, were from Yopitzinco, another city-state in the mountains that were never conquered. Towards the East, between the Aztecs and the Mayan regions were the Mixe, said to be a colony of Andeans from South America, they were insulated from complete conquest by the Aztecs or Zapotecs due to the highland geography. Like the organizational map that Denis linked, there are many city-states and tribes throughout Mesoamerica, these would've been some of the main ones, but the pattern is similar throughout politically for all the others- The Triple Alliance sought tributary conquest and prisoners.
Further reading: https://en.wikipedia.org/wiki/History_of_the_Aztecs
Book: "Aztec Imperial Strategies" By Mary G. Hodges
