Do we accept action at a distance though? As far as I know it still causes some scratching of heads. How does gravity act at a distance? Don't people still look for some exchange of material (gravitons, or whatever - I don't know) to explain it?
Whether there is action at a distance depends on the interpretation of quantum mechanics, meaning that the short answer is: we do not know. However, if there is action at a distance, it cannot be used to transmit information. So for practical purposes the answer is no.
Gravity is theorized to not act at a distance and its field is supposed to be travelling at the speed of light. This results in the prediction of gravitational waves, but have no direct evidence for them yet.
We have gravitons, which are 'things' after a fashion (at that level, the difference between particles, being things, and waves, being disturbances in other things, is usually academical and unknowable) - but then there's quantum entanglement, which is extremely confusing.
Gravitons are just a conjecture so far. Whether the gravitational field is quantized (i.e. has gravitons) or not is one of the big question in physics.