How does a circuit work in a electron's or hole's world?

[Kimly]

We've learned a lot on how a circuit works in a LPM system,and some may also have learned how the BJT works in the carriers' world. But what confused me is how the circuit works in the carriers' perspective.

Say how does the electron transfer in the metal line,and how when it comes to a resistor 、capacitor、inductor, also how in the battery or power system?
Does the power system supply electrons and holes for circuit?

I can only imagine that the electron transfer in the metal line because of the electric field along the metal line.