If you add up all the stuff we see in the Universe (stars, planets, kittens, etc. also called baryonic matter) and compare that to the estimated amount of stuff that actually makes up the Universe, you find that the stuff we can see makes up a paltry 5% of it. Only 5%! Where's all this other stuff, then??? Part of the answer is "dark matter". 

Dark matter was first hypothesized about in 1933 by a crotchety old astronomer named Fritz Zwicky. He argued that adding up the masses of the individual galaxies in clusters did not come anywhere close to the total mass of the cluster itself. Therefore, some of the mass was missing.

In the 1970s, astronomer Vera Rubin measured the rotational velocities of spiral galaxies and found that they were rotating at a roughly constant velocity all the way to the edges of the galaxy. The problem with this is that galaxies are not solid objects, thus they have differential rotation (they rotate at different speeds depending on how far you are from the centre). Physics says that the rotational velocity should depend on two variables: the distance (radius) from the centre and the mass interior to a circle with the same radius. As we move outward from the centre, we only add a little bit of mass, but we add a lot of radius, so the velocity should decrease. But Vera Rubin's discovery says different! The rotation stays the same, so we are adding a lot more mass than we think—but still, we can't see it!

This is the crux of the missing matter problem. Physics is telling us that a large part of our Universe is something we can't see, but it seems to interact with everything else through gravity. But how do we test if it's really matter we're missing and not just a fundamental misunderstanding of physics? The answer comes in the form of the Bullet Cluster.

The Bullet Cluster (pictured below) is the result of a collision between two galaxy clusters. The gas in the each of the clusters, made of normal everyday matter (remember, baryonic matter), slammed into the gas from the other cluster. During the collision, it got heated and glowed in the X-rays (pink in the image). Part of Einstein's Theory of General Relativity says that one of the effects of mass is the bending of spacetime. This sounds complicated, but never fear! Basically, an object with mass can bend space around it. Proof of this came in 1919 when scientists observing the Sun during a total solar eclipse saw stars that were known to be behind the Sun! Galaxy clusters do something similar, acting as a "gravitational lens". Through this effect, we can see the stetched out and magnified arcs of distant background galaxies from behind the cluster. By carefully modeling the lensing arcs, scientists discovered that most of the mass was not between the two clusters with the hot gas. Rather, it had passed through the collision unimpeded (shown in blue in the image). Thus, most of the mass of the two clusters was dark and made of something that would not even collide with other stuff.

Today, we know that baryonic matter makes up approximately 5% of the Universe, dark matter makes up 23% and some new mysterious substance called dark energy makes up the remaining 72%. We actually live in an era of the Universe dominated by dark energy! What is this dark energy and what is it doing? That's a story for another time.

Image Credit: NASA/CXC/M.Markevitch et al.; NASA/STScI; Magellan/U.Arizona/D.Clowe et al.; ESO WFI