The Origins
The Aztecs originate from the Mesoamericans of Mexico and are known as Mexicas, they came from Aztlan, which translates as the place of origin. They fled Aztlan to then settle in the "Valley of Mexico," during the 12th century. They faced problems because upon arriving in the Valley of Mexico they soon came to realize that the Culhucan civilization was already a strong force that controlled the south of lake Texcoco. Their other threat came from the Azcapotzalco, who controlled the west side of the lake. Choosing Chapultepec as their home, the house warming didn't last long, as they were removed by the Tepanecs and instead allowed to settle in the barrens of Tizaapan.
This soon changed, in 1323, when the new Culhuacan ruler lashed out at the Mexicas in a bewildered rage. The Mexicas had requested to make his daughter a goddess and ended up sacrificing her. Needless to say, the ruler wasn't tolerating the Mexicas anymore and banished them from the area. The next place they settled is said to have been chosen due to a sign they witnessed: the crest of Mexico, the eagle perched on a spiky pear cactus with a snake in its talons. It was on the west side of the lake, and it was named Tenochtitlan. There was another Mexica tribe that settled nearby and was soon absorbed into the Tenochtitlan. It was around this time that the Mexicas chose their first Tlatoani, which is a leader or king of the Mexicas in Tenochtitlan.
The Triple Alliance
In the beginning, the Mexicas hired themselves out as mercenaries, between 1370 until 1427. In 1425, Tezozomoc passed away. He was the ruler of Azcapotzalco, who was taken over by Mextla. The original Aztec rulers were Acamapichtli, Huitzilihuiti and Chimalpopoca, whom some believe to have been killed by Mextla. The response was the triple alliance, which consisted of Acamapichtli, Itzcoatl and Nezahualcoyotl, who captured Mextla and sacrificed him.This victory over Tenochtitlan was the boost needed, which led to the next 100 years of their dominance of the Valley of Mexico. It also put Tenochtitlan at the forefront of the military responsibilities making their city the most powerful in the Valley of Mexico.
Itzcoatl and Nezahualcoyotl then sought to expand their territories, heading south and taking over cities, such as Coatlinchan and Tepoztlan, to name only a few. The sons of Huitzilihuitl, Tlacaelel and Moctezuma I, were the main architects of the Aztec empire. Moctezuma I was the successor to Itzcoatl, though Tlacaelel used his power to reform some aspects of Aztec culture, e.g. religion.
The Great Temple
Moctezuma I had to re conquer towns that had strayed from his control and had the intentions of building a great temple, for which they requested donations. Chalo didn't want part of this and there was a war that followed. This wouldn't be the end of the conflict, though, as there was a battle against the Mixtecs of Coixtlahuaca, who were also conquered though notably had received help from Tlaxcala and Huexotzinco.
Tlacaelel demonstrated his power by strengthening the belief of the Aztecs being chosen people to serve a purpose to god. His other actions included the significance of human sacrifice starting the flower wars (where the Aztecs fought against Tlaxcala and other states). Tlacaelel passed away in 1487 but had set the path for the Aztecs as rulers of the empire.
Moctezuma I's son, Axayactl, took over upon his passing and tensions rose over his sister, who was married to the Tlatoani of Tlatelolco, as it was said she had been mistreated. War broke out with Tlatelolco and they were aided by the enemies of Tenochea, though their efforts were in vain as they lost and the rulers of those aiding Tlatelolco were executed.
The First Fall & Spaniards Arrival
1479 brought about significant change as it was when the Aztecs suffered their first loss in battle. This was at the hands of the Tarascans. Axayactl's son Tizoc took over power in 1481 after his father passed away but only brought forty prisoners back from his ceremonial war which was with the Otomies. Therefore his younger brother Ahuitzotl took over. He reigned from 1486 until 1502, taking over vast territories and interestingly inviting the leaders of states, such as Tarascans, Tlaxcaltecs and the Huexotzinca to the enlarged Great Temple ceremony. Among his aggression for taking over land, he also was on top of his defense, creating garrisons and fortifications to protect his people. The Spaniards arrived in 1519 and only three years later they had conquered the Aztecs. Cuauhtemoc surrendered in 1521 with heavy losses on both sides due to the conflicts and the diseases, e.g. smallpox, which spread over the Aztec empire.