When Thomas Young (1773-1829) showed that light created interference patterns and so could only consist of waves, and when James Clerk Maxwell (1831-1879) generalized this into the theory of electromagnetic radiation, both assumed the ontological principle that, since a wave was the deformation of a medium, there would have to be a medium for light or electromagnetic radiation. That was called the "luminiferous" (light bearing) "ether" (aither, Aristotle's fifth element (http://www.friesian.com/elements.htm), of which the heavens consisted). Since the speed of a traveling wave is measured in the inertial frame of reference of its medium, this implies that the velocity of light occurs relative to the velocity of the ether. Ideas about the "ether wind" and how the velocity of the earth through the ether could be measured by measuring the velocity of light in different directions (which was the Michelson-Morley experiment) could then be inferred from this theory.
There were, however, logical problems with the idea of the ether. Electromagnetic waves are transverse or shear waves, not like the longitudinal or pressure waves of sound. Transverse waves only exist in a solid medium. There are no transverse waves in air or water; but they do exist in the earth itself. Indeed, the basic bit of evidence that the core of the earth is molten comes from the fact that transverse (S, shear or secondary) waves from earthquakes do not pass through it, while pressure (P, or primary) waves do. It also happens that the velocity of a transverse wave through its solid medium is proportional to the rigidity of the medium -- the more rigid, the faster. Since light is extremely fast, the ether must be extremely rigid. So notice: How can there be an "ether wind," and how can the earth "move through the ether," when the ether actually must be both solid and extremely rigid -- indeed, the most rigid thing, since light is, even to Maxwell, just about the fastest thing? This circumstance is not noticed when people continue to refer to the ether as some kind of gas, or, with at least a recognition that it would have to be a solid, as something like "jello" (as in Richard Wolfson's video physics lectures [The Teaching Company, 1996]). Jello is not very rigid (to say the least).
Now, it turned out (from the Michelson-Morley experiment) that the velocity of light in a vacuum was the same however it was measured, which made it look like any inertial reference frame was at rest with respect to the ether. The velocity of the earth, or anything else, could not be measured relative to the ether. (And the earth could not simply be carrying a patch of ether along with it, since the phenomenon of the aberration of starlight shows that the earth intercepts starlight at an angle, which would not happen if light were passing through the earth's fixed path of ether.) Albert Einstein then made it the basic postulate of Special Relativity that the velocity of light, which was implied by Maxwell's equations, would be the same in any inertial frame of reference, just as all the consequences of Newton's equations were the same in any inertial frame of reference. "Galilean Relativity," which abolished the absolute velocity of rest, is thus following by Einstein's Relativity, which posits the absolute velocity of light. We could forget about the ether.
Yes, we could forget about ether when it came to providing a frame of reference for motion, but there was still the original consideration that "since a wave was the deformation of a medium, there would have to be a medium for light or electromagnetic radiation." Now, when we consider that it would be impossible for the earth to move through a solid, rigid medium, we could say that this of itself made the ether metaphysically untenable. However, Louis de Broglie later proposed that matter behaves like waves also: particles create the same interference effects as light, and in quantum mechanics particles can "mix" in ways that can only be explained by summing or subtracting their wave functions. Then, in Paul Dirac's theory of the particle, it turns out that particles, as particles, only have location, not extension. What fills space are fields; and fields are, well, a good question.
But, if particles are themselves waves, then they also require a medium. The earth would then not be moving through the ether, it would be, like light, a deformation of the ether. If, that is, a wave is a deformation of a medium. Now, according to Einstein's approach, fields are curvatures in the space-time continuum. That makes space-time sound, not just substantial, but malleable; and all this makes it sound as though the only thing that fills space is space itself, which is the substantial substratum of all matter and energy. This would not be a disagreeable thought to Descartes (http://www.friesian.com/hist-2.htm#descartes), to Spinoza (http://www.friesian.com/spinoza.htm), or to Parmenides (http://www.friesian.com/greek.htm#parmenides). What space would then be was thus originally answered by Parmenides: Being itself.
Parmenides did not necessarily identify Being with space himself, but he did think of Being as extended, and his denial of the existence of nothingness, which could mean empty space or the vacuum, became a dominant consideration in the history of philosophy. When either Empedocles or Descartes denied the vacuum, they were following Parmenides. However, where Empedocles had filled space with four elements, Descartes gave matter just one attribute, extension. This unified matter more like Democritus than like Empedocles. Ironically, the modern conception of matter, which in a sense begins with the atomic theory of John Dalton (1766-1844), modified Democritus in the direction of Empedocles, positing discrete and independent atoms in space, but with the provision that these atoms are of different elements -- not the four (or five) classical elements, but the substances experimentally separated by both alchemists and modern chemists.
The empty space of Democritus and the absolute space of Newton seemed vindicated by 19th century physics. When Einstein allowed the theory of ether to be dropped, however, this was interpreted by many who were aware of the philosophical debates (http://www.friesian.com/space.htm#clarke) between Newtonians and Leibniz (http://www.friesian.com/leibniz.htm) as a refutation of independent Newtonian space altogether. Leibniz's theory of space, however, hardly seems suitable to modern physics. Leibniz denied the existence of space because he denied the existence of matter and even of real extension. All that existed for Leibniz were the "monads," which were essentially little atoms of consciousness. This does not sound like anything that Einstein, or his interpreters, would have had in mind.
What the philosophical interpreters may have had in mind, really, was not Leibniz, but Hume (http://www.friesian.com/hume.htm) -- not a different metaphysic of space but simply skepticism, that space has no independent reality because it is subjectively "constructed" (which is not what Hume said himself, but is how Hume has tended to be read in the 20th century). Not even Kant's (http://www.friesian.com/space.htm#kant) theory, that space is a subjective but fixed condition of perception, was seriously entertained. On the other hand, as has been noted, Einstein's view of space-time could just as easily be taken to imply that space is substantial in a fashion closer to Parmenides or Descartes. Again, this direction seems to have been largely shunned in philosophical intepretation, which was driven by skeptical presuppositions.
An interpretation of Relativity, however, let alone an entire philosophy of science, founded upon skepticism, always ran the risk of the slide down the logical slope. If space is subjectively constructed, and perhaps arbitrarily so, then so can all of science be. The skeptical tendency of 20th century philosophy then logically led to deconstruction (http://www.friesian.com/hermenut.htm) and all the ways in which all of science can be dismissed as an artifact of quasi-Marxist "power" relationships. This has not helped, to say the least, in understanding the nature of space. But if neither Leibniz nor Hume are the answer to Einstein, then the whole matter must be reconsidered in a way that was really never done in the 20th century.