An eventual theory of quantum gravity may entail another viewpoint of gravity as a quantum field and mediated by a hypothetical graviton. But as of now we don’t have a good idea of what such a theory might look like; unifying QM and GR is famously one of the great unsolved problems in physics.
I really hope you meant speed of light there.
Regardless, this thing is still a mystery to me. Why, if gravity propagates at c (or, better perhaps: Changes in the space-time curvature, which is caused by mass-energy, propagate at c), why doesn't the earth spiral into the sun or away from it? If the earth is attracted to the point where the sun was eight minutes ago and not to where it is right now, it's orbit should not be stable. It's a very big difference compared to the "gravity is instant" way of Newton.
Besides this all, I still can't get anyone to give me a clear cut and dried answer on my original question. If gravity is instant in the Newtonian model, and that gives us stable orbits and all that, how does that translate to the Einsteinian model, where there's an upper speed limit of c? So, why would that even work, if the gravity of the sun takes 1au/c to get here and be felt by the earth? Or, is gravity somehow "above" this speed limit?