This is a quote from Optics by Hecht:
A stationary charge has a constant E-field, no B-field, and hence produces no radiation—where would the energy come from if it did? A uniformly moving charge has both an E- and a B-field, but it does not radiate. If you traveled along with the charge, the current would thereupon vanish, hence B would vanish, and we would be back at the previous case, uniform motion being relative. That's reasonable, since it would make no sense at all if the charge stopped radiating just because you started walking along next to it. That leaves nonuniformly moving charges, which assuredly do radiate. In the photon picture this is underscored by the conviction that the fundamental
And from the Wikipedia page on electromagnetic waves:
An electromagnetic field very far from currents and charges (sources) is called electromagnetic radiation (EMR) since it radiates from the charges and currents in the source...
I've always thought of a current as a flow of electrons through a conductor, but here it seems to mean something independent of a medium through which electrons can flow. So what is current in this context?