Conquistadors
The private Spanish adventurers who toppled the Aztec and Inca empires in a single generation, financed by debt and licensed by a crown that paid them in plunder.
In 1519 Hernan Cortes landed on the Mexican coast with about five hundred men and no authorization worth the name. Two years later the largest city in the Americas was rubble and its empire was his. In 1532 Francisco Pizarro walked into the Inca highlands with roughly a hundred and sixty men, seized the emperor Atahualpa in the square at Cajamarca in an afternoon, and held a realm of ten million people to ransom. Both men operated under a crown whose claim to the Americas rested on the Treaty of Tordesillas. Nothing in European military history explains this. The explanation is not military.
Who they actually were
The conquistadors were not an army and not employees. They were shareholders. A leader obtained a capitulacion, a royal license to conquer at his own expense, then borrowed against future spoils to buy ships, horses, and powder. Every man signed on for a share of the take, and the crown took the quinto real, its royal fifth, off the top. Madrid supplied paperwork and legitimacy. The investors supplied the violence and absorbed the risk.
This matters because it explains the behavior. Men who have mortgaged everything and will be paid only in loot do not garrison, negotiate, or wait. They gamble. Cortes famously scuttled his own ships so his men could not vote to go home.
Why they won
Steel, horses, and gunpowder helped at the margin, particularly cavalry against infantry in open ground, but they were not decisive against tens of thousands of disciplined Mexica warriors. Three other things were.
Disease, the deadliest half of the Columbian Exchange, came first and did most of it. Smallpox reached Tenochtitlan in 1520 during the siege and killed a large share of its defenders including the emperor Cuitlahuac. In the Andes it arrived before the Spanish did, killing the Inca Huayna Capac around the mid-1520s along with his designated heir, and triggering the civil war between Atahualpa and Huascar that Pizarro walked straight into. He did not conquer a functioning empire. He conquered the winner of a war that had just ended.
Allies came second. Cortes did not fight the Aztecs with five hundred Spaniards. He fought them with tens of thousands of Tlaxcalans and other subject peoples who had their own reasons to hate Tenochtitlan and who correctly judged that the newcomers were the better bet. From the indigenous side this was not a conquest but a rebellion with foreign auxiliaries, and it took decades for the allies to discover what they had joined.
Decapitation came third. Both empires concentrated sovereignty in one sacred person. Seize him, as Cortes did with Moctezuma and Pizarro with Atahualpa, and the machine stops. A European kingdom with a functioning nobility could survive losing its king. These states could not.
The paperwork of conquest
Spain took the legality seriously, in its own fashion. From 1513 conquistadors were required to read out the Requerimiento, a legal notice informing listeners in Spanish that they were now subjects of the Castilian crown and that resistance made the ensuing war just. It was often read to empty beaches, or from shipboard, or at night.
Conquered populations were then distributed under the encomienda, a grant of the labor of a given community in exchange for a promise to Christianize it. It was slavery in everything but name, and it produced Spain's own dissent: the Dominican friar Bartolome de las Casas spent decades documenting the killing, forced the New Laws of 1542, and argued the case at Valladolid in 1550 that the peoples of the Americas were rational human beings with rights. He won the argument and lost the outcome.
The echo
The conquistador model, a state licensing private violence abroad in return for a cut, is the founding template of European expansion. The East India Company and the Dutch East India Company are the same instrument with better accounting. And the silver that Potosi and Zacatecas began shipping in the 1540s did not stay in Spain. It flowed through Europe and onward to China, financing Spanish wars, European inflation, and the first genuinely global trading system. Two years of adventuring by a few hundred indebted men reorganized the world economy.