Can someone list for me some issues that modern day historians might consider the mysteries of classical or medieval warfare? Like, quirks about weapons, armor, or fighting in general that might have been understood by many people of the era, but that for one reason or another is controversial to modern historians.
For example, I remembering seeing a documentary that claimed we don't really know how Vikings even held their swords, because their swords had tiny hilts. I'm not sure if there's a verdict in on Viking swords yet, but I'm looking for controversies like that. Other examples I can think of are how we don't really know what Greek Fire is made of, and I'm told the Romans have a system for rotating exhausted legionnaires out of the frontline and replacing them with fresh soldiers, but we don't know how they managed that in the chaos of battle.
Most historians are not too interested in fighting as such. They are more interested in the social, economic and cultural impact of warfare. So the so called 'hoplite debate' is not about weapons, armor or battle plans but about the growth of the polis as a political unit in ancient Greece.
Even as far back as George Grote (1846-56 A history of Greece), his ideas are really about how warfare reflects political changes from monarchies to republics. He is concerned with farmers and agriculture not how a sword can cut flesh or how units moved around on a battle field.
Looking at the development of Greek warfare, not for the sake of studying warfare itself, but as an indication of political change (in particular the rise of tyrannies an then democracies) can be found in the work of Nilsson, Lorimer and Andrewes. Even more recent works which attack the 'hoplite orthodoxy' (such as by Snodgrass and Cartledge) are still only using hoplites to talk about political and economic debates.
So in short the controversial debates among historians relating to classical warfare are rarely to do with the details of fighting (which preoccupy documentaries about the ancient world) but are to do with how the world developed and how warfare can illuminate this. Debates about hoplite formation are less controversial than debates about the social status of farmers who would have to fight as hoplites occasionally, or what it meant to be a citizen of a polis.
This is not really my area so I couldn't tell you specifics regarding these social, economic and political debates but a good place to start is Kagan and Viggiano's opening article in Men of Bronze. It gives a good summary of the entire debate regarding the emergence of the hoplite as a weather vane for larger cultural changes in Greek society.
An important one regarding the Roman military is how we are supposed to conceptualize the changes between the Early Empire and Late Antiquity: were these changes force by circumstance, a result of the need to recruit more soldiers, faster due to increased external and internal threats all over a continually shrinking economic base? Or were they rational responses to the new needs of a mature empire that was no longer expanding? My sense is that historians with a focus on military history proper (such as Garrett Fagan) tend to be fairly pessimistic about the performance of Late Roman legions, but it is a topic that still has quite a field of debate.