From action at a distance to gravitational waves
In Newtonian gravity, as in electrostatics, the force on one body depends on the current position of another. This fiction is satisfactory so long as the bodies move much more slowly than the speed of light. The force between fast-moving bodies cannot depend on the current positions because information about locations cannot travel faster than the speed of light. In fact when we suddenly move a body, there must be an expending spherical shell around the body in which the gravitational field associated with its old location morphs into the field associated with its new location. When this idea is worked up mathematically we conclude that a body communicates directly with the vacuum just around it, which communicates with the vacuum a bit further away, and so on, until eventually the second body is reached and it experiences the updates force. Action-at-a-distance has given way to coupling to a dynamical vacuum, and gravitational fields are reconfigured by waves that carry energy and momentum. Gravitational waves are a bit more complicated than electromagnetic waves (tensor rather than vector modes), and they are harder to generate because it's hard to get massive bodies moving relativistically. Not too hard for Mother Nature, however!