Capacitor dielectric and current flow
I think I hear the sound of a can of worms being opened.


It's called displacement current - it is a time varying electric field that gives rise to the same phenomena associated with regular currents. For the casual onlooker it might as well be real current.

It's embodied in Maxwell's equations. 

Wikipedia on the subject

Another electrical phenomena that apparently should have real current but doesn't is the radio wave. Again all down to Maxwell and displacement current.