This aether drag hypothesis was an attempt by classical physics to explain stellar aberration and the Fizeau experiment, but was discarded when Albert Einstein introduced his theory of relativity.
When more realistic assumptions are made (that real objects are composed of particulate matter, and have gravitational properties), under general relativity's more sophisticated model the resulting descriptions include light-dragging effects.
Einstein's theory of special relativity provides the solution to the Fizeau Experiment, which demonstrates the effect termed Fresnel drag whereby the velocity of light is modified by travelling through a moving medium.
Einstein showed how the velocity of light in a moving medium is calculated, in the velocity-addition formula of special relativity.
Einstein's theory of general relativity provides the solution to the other light-dragging effects, whereby the velocity of light is modified by the motion or the rotation of nearby masses.