Space is not empty but is in fact a fabric or medium that propagates magnetic fields and electromagnetic waves. Space is not matter in the sense that it is not composed of particles.
Tendencies are to describe space in terms of plasma.
This because plasma too will propagate electromagnetic fields and carry electric charges. This view though closer to the truth than the concept of empty space is still not completely accurate. A plasma is made up of particles. Space exists between particles. When you look at a solid object it is really not solid at all.