"Knowledge of what is does not open the door directly to what should be."
– Albert Einstein 
(Image Credit: NASA)
There’s a search going on that started at the beginning of the 70’s, when observations revealed that something wasn’t quite right with the universe – part of it was missing! 
The reason that we know it’s there is because of its effect on what we can actually see. To start with the stars at the edge of galaxies are moving to fast, there seems to be extra stuff exerting an influence. This stuff might be invisible but we know it's there. If it wasn’t there there wouldn’t be enough gravity to hold the stars together and everything would fly apart and chaos on a galactic scale would ensue.
Another piece of smoking gun evidence, is an optical effect observed around some distant galaxies. When the Hubble Space Telescope was pointed towards the massive Abell Cluster 2218, the gravity pull around it was so great it actually bent light around it, turning the whole region into something known as a gravitational lens. Using this technique Hubble was actually able to see through it, regions at the very edge of the universe. It took some amazing images such as the one above, stuffed full of galaxies. However, once various measurements were taken, it was soon realised that the light was being bent too much. In other words the combined mass was greater than anything that we could measure, meaning a lot of the mass was invisible. As far as dark matter is concerned we believe to be around 25 percent of the mass of the universe.
So what could dark matter be? The best guess is that it’s some sort of exotic hidden particles we are yet to discover. 
But this isn’t all that’s missing. There’s another 70 percent lost back down the back of the galactic sofa and we have labelled this dark energy. We have even less idea about what this could be. We are just starting to understand that space isn’t nothing, but is instead a rich area stuffed full of dark energy, whatever it might be.
So if you do the sums, that means there’s 5 percent that we can see and currently understand. That’s the observable universe today. So when you see those Hubble images, etc, we really are just seeing the peek of a very big iceberg, the rest floating beneath the visible waterline.
The below YouTube video provides a very neat overview of all this missing stuff.