Aether drag hypothesis Updated +Created
Given experiments such as the Fizeau experiment and the Michelson-Morley experiment that couldn't really detect the Earth's movement across aether, people started to wonder if the Earth wasn't dragging the luminiferous aether.
Luminiferous aether Updated +Created
Can you just imagine what if luminiferous aether was one single fixed rigid body? This is apparently what Maxwell believed, Subtle is the Lord by Abraham Pais (1982) page 111 quoting his entry to Encyclopedia Britannica:
There can be no doubt that the interplanetary and interstellar spaces are not empty but are occupied by a material substance or body, which is certainly the largest, and probably the most uniform, body of which we have any knowledge.
Then it would provide a natural space coordinate for the entire universe!
Apparently Einstein was the first to completely say: let's just screw this aether thing completely then, it's getting too complicated, and we don't really need it. As Wikipedia puts it well, in very unencyclopedic tone[ref]: Aether fell to Occam's razor.
Polarization of light Updated +Created
This section discusses the pre-photon understanding of the polarization of light. For the photon one see: photon polarization.
People were a bit confused when experiments started to show that light might be polarized. How could a wave that propages through a 3D homgenous material like luminiferous aether have polarization?? Light would presumably be understood to be analogous to a sound wave in 3D medium, which cannot have polarization. This was before Maxwell's equations, in the early 19th century, so there was no way to know.