Further Conifold's Comment:
"Electromagnetic field is self-propagating, changing electric field creates magnetic field in its surroundings, and then magnetic field does the same for electric field. Original theory was that electromagnetic field propagated in ether, but properties of ether had to be made paradoxical to account for observed behavior, so ultimately it was discarded."
I'd like to add: don't confuse "emtpy space" and the philosophical notion of a void or "nothingness". Spacetime is made of material things with definitely observable properties (e.g. this piece of spacetime over here can have a different curvature tensor, and thus measurable geometry, from that piece of spacetime over there). Those material things which are the "stuff" of spacetime and physical existence are quantum fields, and modern physics believes that there are only a handful of them (the EM field, the electron/positron field etc). "Empty space" is a linguistic "shorthand" that describes the state of local spacetime when all quantum fields locally are in their ground states: there are "no electrons or positrons" in it is the same as saying that the electron field is locally in its ground state), there are "no photons" is the same as saying that the EM field is locally in its ground state and so forth. The quantum fields are still there. Observable "stuff happens" in physics when these fields interact and change state: e.g. the electron field may drop to its ground state from one where there is "one electron and positron" locally and thereby cause the EM field to rise to a two-photon state in an observable event we call "mutual annihilation".
These quantum fields are not thought to be "in" or "embedded in" anything, i.e. a void. Modern physics finds no need to postulate an extra "thing", i.e. empty space, further to the quantum fields that make up existence.
So the EM field in its ground state is always "there", permeating all of existence and ready to transmit light. This has some likenesses to the notion of an aether insofar that there is a material "thing" doing the propagating, but because the EM quantum field shows fundamental symmetries like the ones I talk about here and also here, the EM quantum field does its work in a Lorentz-covariant way and such that there is no preferred inertial frame, in contrast with a material medium whose presence would give rise to a preferred frame. You are just as much "at rest" relative to the EM quantum field in any inertial frame as you are in any other, in contrast with the situation where there is a material non-ground state medium, where there would be a measurably determined unique frame which would be at rest relative to the medium.