(Mainly focusing on historiography of the pre-medieval period, but later subjects are not out of question)
Continuing in my series of contrarian-ish attacks on the perceptions about warfare in much of modern mainstream historiography and popular perceptions, I've got something to say about organization. You see a lot of historians, particularly where antiquity is concerned and even on this very board, go into great detail when describing the structure of units by precise numbers and theoretical battlefield formations.
Now, as I've already established, battlefield formations are hardly the most important thing about a unit, due to the relative rarity of such set-piece engagements - and hardly a topic worth spilling endless words over. The other factor, seen as the defining characteristic of a unit by many historians of a purely philological background, is its size, in numbers of men. Just how far from truth it actually is can be seen just by looking at something right in front of our noses - modern armies and early-modern ones. Units are more often far under their theoretical strength than not, and sometimes there is no such thing as theoretical strength for some levels of organization. So units are neither about their numbers, or the way they are arrayed on the battlefield. What the hell are they defined by, then? The answer couldn't be simpler - their role.
By looking at armies throughout history, a pattern can be discerned - the distinction between various levels of command, namely, the individual, the tactical (generally on a couple of levels), the operational and the strategic, as well as the distinction between units primarily administrative and primarily tactical in nature. In many cases, there might be strong parallels with modern organization, even if there is quite a bit of overlap due to the notable difference in size. Still, the point stands: a unit is defined by its purpose, not the details of its operation and strength.
The typical organizational tropes, with modern names:
-The squad: a small group of men, usually composed at the gathering of a larger element, but sometimes pre-composed, which is more or less indivisible, together in all deployments, tasks and mundane life.
-The regiment: a unit that hugely varies in size, and forms the administrative building block of an army, rather than a sub-division. It might also double as a tactical unit in some cases.
-The battalion/brigade: the basic large-scale tactical unit. Formed by dividing administrative units (battalion) or grouping them/tactical detachments of such (brigade). Both can also be the regiment at the same time.
-The company: an administrative sub-unit of the regiment.
-The platoon: a tactical sub-unit of the battalion, sometimes (but rarely) brigade, used for low level command.
-The division: an operational/administrative unit, formed by grouping numerous tactical/administrative units from the larger whole of an army, or alternatively acting similarly to a regiment, but on a scale large enough to potentially act as an operational level unit.
-The corps: an operational/strategic, sometimes administrative unit, which is large enough to act with a great degree of autonomy, but still forms a part of a larger force and can act as part of it. Can be formed both as a group of smaller units with some common characteristics, or by detaching units from the larger whole. An ambiguous designation for anything that isn't modern.
-The field army: the strategic and administrative whole that acts as an autonomous unit in the field, used to accomplish strategic goals. Can be permanent and ad hoc alike.
Now, for an example, let's see the Roman mid-era army.
-The squad = contubernium/decuria
-The platoon/company = century/turma
-The battalion = cohort/ala
-The regiment/brigade = legion, auxiliary cohort, ala
Larger units formed in a generally ad hoc manner.