Many people have heard that at the end of the 19th century there were small anomalies in the observed location of the planet Mercury. It was apparently not quite where it should have been, had Newton's theories of gravitation been entirely correct. Einstein proceeded to modify Newton'ts laws somewhat and it was discovered that with these modifications the observed locations of Mercury were now spot on. Score one for Einstein.
Toward the end of the 20th century, small gravitational anomalies have been once again observed, this time in the behavior of very large objects in space. Rotating galaxies, for example, are not quite rotating as they should if the Newton-Einstein formulas are entirely correct. Likewise, orbital velocities of galaxies in clusters are not as they should be. Two possible explanations have been proposed, either that there is a better theory of gravity to be had (though nobody seems to have a good idea of what this might be) or that there is a lot of matter, type unknown, out there which would account for the anomalies observed without any change in the (extremely accurate and well-tested) Theory of Relativity. This is the so-called dark matter, the idea being that there's some sort of unknown stuff out there which we can only observe at the cosmic scale, because for reasons unknown it doesn't show up in anything around us we know of.
Now the evidence is apparently in, as a collection of astronomers using a constellation of our most advanced telescopes has announced direct observation of dark matter. Your tax dollars at work.
Don't worry, there's still the even more perplexing mystery of dark energy to ponder....
Connecting the dots on the video
10 minutes ago