Explanation notes on the multipole expansions of the electromagnetic field

Starting from Jefimenko's equations, we consider the multipole expansions of electric and magnetic fields for a confined system of charges and currents. We analyze and comment on the calculus of radiated power, on the consistent use of approximation criteria, on the invariance of physical results when changing the point of reference, as well as on the use of electric and magnetic moments described by symmetric and trace free tensors.