Cycling and rotating divisions... air raids... mountain-specialists... efficiency penalty for HARM... leaders and troops getting EXP... As a CK2 and EU3 player, HOI3 stuff like that intrigues and frightens me.
I don't completely understand all the systems at 500 hours, but that's ok, because you don't really have to on normal difficulty against the AI. I'd probably get rolled in mp against skilled players though.
The combat has some similar concepts to EU, like combat width, which controls how many units fire at each other in a battle in EU. In HoI, each unit has a width (e.g. infantry - 1; armor - 2), and each province has a total width that can be filled by those units. If you have 200 divisions on one province, 99% of them will be idle because there isn't enough width to participate in the battle. Not that you'd ever want to have that many, but just as an example.
Battles can have divisions leave and get replaced by other divisions. The German divisions would wear down their organization (like EU's "morale") and take casualties, then leave to rest+reinforce somewhere else while a fresh division took its place. Thus they could sustain the meat-grinder for a very long time. The reason they did this was because "lol dumb AI".
HARM is "heavy armor". There's tons of brigade types in HoI, whereas in EU you only have infantry/cavalry/artillery, here you get (off the top of my head) cavalry, mountaineers, marines, infantry, militia, engineers, artillery, anti-tank, anti-air, self-propelled artillery, rocket artillery, tank destroyers, light armor, armor, heavy armor. You build your divisions using these elements, then you have a variety of divisions on the field. Each division can belojgn to a corps, which can belong to an army, which belongs to an army group, which is subordinate to a Theatre head quarters. You can actually automate these HQs to take over for you. And actually you can automate pretty much everything, technology, production, diplomacy, espionage etc.
Combat is way more interesting than EU, for sure. Also far more complex. It's often about taking advantage of low level terrain features, establishing lines, planning b reakthroughs, encircling the enemy, etc. Managing logistics with supply+fuel can be really hard to get your head around when something will or will not cause a problem unless you take the time to learn the intricacies of reading the supply map mode, which you kind of have to look at over time to notice where bottlenecks are occurring and so on. I can't be arsed doing that, even with all my time played lol.