One of the great puzzles of history is why the Spanish were able to conquer the Americas. Not only did they take control, but they did it comparatively easily with just handfuls of conquistadors; plus they did it thoroughly, influencing the language, the religion, the demography, the institutions, and so much else. Arguably they created an entirely new civilization: Latin America.
The blog Living Anthropologically runs through some current thinking on the subject. Horses, guns, and literacy probably gave the Spanish few advantages. The real secrets to their success were disease, steel swords, and particularly native allies.
That last one makes reasonable sense. One reason the British conquered India is because of its political disunity and the native allies they obtained. Anthropologists apparently like this explanation because it is politically salutary: it makes the indigenous people, or some of them, appear as active agents rather than passive victims.
But it raises more questions: why was there political disunity among the populations of the Americas? Why were their polities fragile, or to say the same thing in different words, why did they not have higher levels of cooperation?
Once in control, the main reason for the comprehensiveness of Spanish influence was the demographic expansion of the Spanish into the New World.
(h/t Marginal Revolution)