Hi Lejuste
It is true that in any case, magnetism almost takes magic
who has not marveled at these invisible forces?
However, we can say that they are relatively well mastered
for example; with the race to waste energy, electric motors display phenomenal efficiency, around 95% !! proof that the "magnetic circuits" are perfectly mastered
We know how to create a magnetic field from the displacement of a known number of electrons in a coil which is also perfectly quantified, and the theory works perfectly to the point that it is reproduced in all common equipment.
For permanent magnets, the concept is different (whatever)
but we know that the origin is "in" the electrons, the famous "SPIN" or orientation
I no longer know where it was specifically discussed on the forum
See also how we make permanent magnets :
http://fr.wikipedia.org/wiki/Aimant_permanent
Now, to answer you and in my current opinion, I do not think that we have a perfect grasp of the concept, without which, we would have already found how to link quantum mechanics to macroscopic sciences (I know it is badly said)
But I think that the expression of magnetism on our scale is the fruit of particular quantum phenomena.
You know, the 4 fundamental forces discovered to date:
-------------------------------------- Relative intensity
Strong interaction (nuclear) ----- 1
Electromagnetic interaction -10exp (-2)
Weak interaction (nuclear) --- 10exp (-13)
Gravitational interaction ---- 10exp (-38)