Some religious tenets give combat bonuses as well.

I noticed this too, I think it is from an overpowered event. It's one of those 3 options events, one of the choices is +7 attack, it comes in the Classical era, which makes it hugely OP. The AI got it in my game and thier warriors were a match for my veteran swordsman, very irritating. Of course they declared war during it. Needs to be nerfed down to like 3, 4 max. It's not religion as others have stated because that is +2, it gives you the full breakdown of what a unit has, like veteran, high ground, tenet etc. I'm 90% sure it is from an event. 

It's probably an event (or ransacking bonus?), but it's possible to stack permanent combat strength quite high. I think the list is:

Base: 22

Hun Legacy Trait (+2 to Cavalry): 24

Difficulty (+2 or +1): 26

Homeland Ideology (possible +2, but likely only +1 in Classical): 27

Professional Army Civic (+1): 28

Veterancy (+2 or +1): 30

Hittite Legacy Trait: 31

There is a Neolithic event that gives a permanent +2 as well. Which I posted a thread about already because that is freaking insane. 

Promethian wrote:

There is a Neolithic event that gives a permanent +2 as well. Which I posted a thread about already because that is freaking insane. 

Which ones that?

There can also be ai bonus modifiers depending on the difficulty, they have been a bit notorious in Amplitude games.

It's the ferocious +7 trait from an event. Lasts ten turns I believe. 

Depends on the game speed, it's 20 turns in the Endless and, damn, do I have a bone to pick with it after last playthrough. Had a scuffle with Romans over new world, fully Medieval army on my side, mostly legionaries on theirs (not even Praetorian, just what their generic Swordsmen look like, which is mighty cool, may I add), so it didn't even come to me to check their strength, though I should, because terrain was disadvantageous to me. My Pikemen and Crossbowmen just melted, no mercy, good thing I had Teutonic Knights.

Has anybody mentioned the AI have biases and traits? Some of them should provide bonus to combat strength or speed.
Check carefully the AI you are playing against when you are setting up the game.

On Humankind level, the AI gets +2.

The ferocious events (+7, and also the one with +14 no one seems to complain about) can be very nasty. But they only last for 10 turns. So in many circumstances, the best way of dealing with them is avoiding fights for that time. It's important to notice them on the enemy units before battle though, and not be surprised by it when you massed some units for a decisive battle...

Remember you can stack those bonus as well, if you always choose the science/economical/industry bonus, your unit will be behind in term of strength. Civics, tenets, cultures, defending, etc, if you neglect military, you will sooner or later face difficulties. Russians -> Soviets can easily get a +10/11, if they have enough territories / stability.

If you have no military bonus, you have to loose, because it is fair: a weak army should not beat a strong army... Unless you lake really good tactical choices (stay behind walls to fight horses, so they can't attack you for example)