There are a couple of reasons why people react with puzzlement to ideas like General Relativity. The idea of "spacetime" is difficult enough to picture, without talk about the idea that mass distorts it the way a bowling ball distorts a trampoline. (Note to self: Promote trampoline bowling as the world's new most dangerous sport.) How can you prove that a warp in spacetime actually happens?
Einstein's theory says that large objects will create greater amounts of warping. That, in turn, would mean that light could be delayed, depending on what lies near its path. In 1964, Irwin Shapiro managed to test this on a cosmic scale.
Initially, Shapiro's experiment involved looking at faraway stars, and how the image of them changed as other objects moved in front of them. For example, a star that might appear right on the edge of the sun, from one vantage point, might seem to jump as the sun moved in front of it. As its light moves toward the sun, it will get sucked into a sort of half-orbit, like a piece of debris briefly getting sucked in the swirl of water around a drain in a sink, before being flung forward again on a slightly new path. That new path will intersect with Earth and make the star look like it's in a different place than it was before.
But calculating relativity using the position of far-flung stars involves a lot of variables, and the resolution of telescopes has limits. So in 1964 Maximilian Shapiro came up with a new way of testing the idea. He would fling radar signals toward Venus and Mercury, bouncing them both off each planet and measuring the time they took to get back to Earth. He would do this in positions that would mean that their paths could get warped to different degrees by the gravity of the sun. As the path is curved, it becomes longer, and the radar would take more time to get back to the Earth. Since time can be measured very accurately, it was easy to measure the time delay — and confirm general relativity.
The delay, when they measured it, was only 200 microseconds, but it was enough - and within predictions - to show that the mass of the sun really did delay the light coming back to Earth.
Since them, version of the Shapiro time delay experiment have been used using different media and different celestial objects. As technology improves, it gets more and more accurate results. It's one of the classic experiments that proves Einstein's general relativity.
Image of Venus: NASA/JPL