I don't know anything about this and am* excited to see some answers but when you say Queens do you mean women who were in power or women who were the wives of Kings?

If I may piggyback on to this question: What do you know about women in seats of power in Aztec kingdoms? Could they assume any type of official roles in bureaucracy, religion or the military?

I must preface this by saying that it is an incomplete answer that really only responds to one part of the asked question. I hope it contributes to a wider discussion though.

From my reading, the most influential power wielded by women was indirect power, realised through their legitimising of the monarch.

Aztec noblemen married multiple women, but the principal wife was "was from a more prestigious family than that of her husband, and her marriage cemented an Aztec noble's relations with a powerful lineage."

So the noble women in Aztec culture were the vessels of power, and only by marrying one could a man become linked to that power. The principal wife was also the bearer of the heir in most cases, presumably because she was a direct descendant of the powerful lineage that the nobleman had sought to join.

Non principal wives came from lower families who sought to make a connection with the ruler(the man who had already elevated his position).

Another ruler married twenty daughters of lords from a certain region, and his children with the twenty became the new nobility. This had a twofold effect: his children were legitimised by becoming a part of local noble lines; and the existing nobles passed their power on to their grandchildren - ceding it from themselves to individuals further down their family line. "In central Mexican political ideology, the legitimacy of a polity was dependent upon the Toltec blood of its ruling dynasty." In essence, without marrying the correct noblewoman, a conquering lord would have no claim to a throne.

So to recap, women were important wielders of power because they held the legitimacy of family lines and noble houses or dynasties. By marrying a noblewoman, Aztec men could increase their position in the social hierarchy and legitimise their children as rulers.

Sources(paywall):

'Women and Political Power: The Inclusion and Exclusion of Noblewomen in Aztec Pictorial Histories', Lori Boornazian Diel, RES: Anthropology and Aesthetics, 2005, via Jstor.

'Sexual Politics in the Aztec Palace: Public, Private, and Profane', Susan Toby Evans, RES: Anthropology and Aesthetics, 1998, via Jstor.

'Lineage, Class, and Power in the Aztec State', J Rounds, American Ethnologist, 1979, via Jstor.

Kingship and Queenship are foreign terms and not directly applicable to the Nahua system of rulership. I'd defer to you in whether or not they would even be anachronistic at time periods in Europe not far removed from the time of Contact.

The best way to understand the structure of rulership in the Aztec system is to understand it more in dynastic prestige and connections. While there were recognized positions of authority -- tlatoani being the most notable for this converation -- the importance of those titles cannot be understood without understanding their enmeshment in the dynastic and ethnic web of Late Postclassic Central Mexico.

By tautological decree, a tlatoani was the ruler of an altepetl (polity, but city-state might be more useful a concept here), and a backwater village became an altepetl by appointing a tlatoani. Not all tlatoque of altepetemeh (Nahuatl plurals are interesting) were created equal, and identical titles could belie the deep play of establishing social hierarchy.

Since that is some high-falutin' talk, let's focus in on the most famous and well known lineage, that of the Mexica of Tenochtitlan, and I'll try to highlight some of the ways women in these dynasties were significant.

The first thing to understand about the Mexica of Tenochtitlan (i.e., the Tenochca), is that they were not the Mexica of Tlatelolco (i.e., the Tlatelolca). A seemingly minor point, but one that starts us off by emphasizing the familial nature of ruling. These literal cousin dysnaties were both allies and rivals, and both polities each had independent tlatoque (at least until Tenochtitlan conquered Tlatelolco in 1473 CE).

The more important thing to keep in mind about the Mexica, in general, is that they were essentially the very tail end of a wave of migration of semi-nomadic people (the Chichimecs) into the Basin of Mexico. The start of the migration could be placed as far back as around the 9th Century CE, but it was really in the 12th C. that it intensified and upended the social order of things, including seeing the previously dominant polity, the Toltecs, collapse. There's a complicated series of land-squatting, battles, and skin-flaying that leads to the founding of Tenochtitlan, but once the city was established and stable to the point that it was ready to elect a tlatoani, it turned to the city of Culhuacan.

Culhuacan is relevant because its ruling dynasty could claim direct descent from the Toltecs, and thus the altepetl was a prestigious, is not particularly dominant, force in the Basin. The tlatoani that was called from Culhuacan was, Acamapichtli, who was of mixed Mexica and Culhua heritage. And here is where it gets a bit complicated.

On top of all the other problems with the paucity of sources and Rashomon-like nature of getting a general history of pre-Columbian history from different perspectives (the major works tend to be biased towards their own ethnic group), there is the inevitable problem that women are, for the most part, invisible. Women are discussed in the abstract, for certain, and Sahagún devotes an entire chapter of his encyclopedic General History... to describing the traits of good and bad noblewomen. The text can be repetitious, but the most significant synthesis is probably this passage:

The noblewoman is a protector, meritorious of obedience, revered, worthy of being obeyed; a taker of responsibilities, a bearer of burderns -- famed, venerable, renowed.

The good noblewoman is patient, gentle, kind, benign, hard-working, resolute, firm of heart, willing as a worker, well disposed, careful of her estate, She governs, leads, provides for one, arranges well, administers peacefully.

More on the estates and governing in a bit, but the point here is that women are more often discussed in the abstract in the histories, while conversely individual men are brought forth into the light of history. When we do get individual women identified, it is either as traitorous figures (who are strangely always named Malinalli) or as the wives of major tlatoani.