"An atomically-thick layer of bonded carbon atoms in a hexagonal array, that can be made by peeling a layer off a graphite block with sticky-tape " doesn't sound like a particularly wondrous material. But that's an approximate description of graphene, which may one day fairly soon change the world.
The material was first "discovered" in its form of isolated thin sheets in 2004 by a group of scientists at Manchester University and the Institute for Microelectronics Technology, in Chernogolovka, Russia. And since then a sequence of scientific discoveries has revealed quite how astonishing the material actually is.
Just recently researchers at Rice University  discovered a way of using a layer of graphene to store electronic data. Nothing new there, you might think: But the graphene memory may have the capacity to store data much more densely than NAND flash is predicted to, and be capable of withstanding 200ºC heat. This might make graphene-based memory an excellent candidate for long-term digital archiving--one current issue in the minds of electronic historians.
Meanwhile, University of Maryland physicists have demonstrated that  graphene can conduct electricity better than any other known material at room temperature. Electron transport in graphene occurs 100 times faster than in silicon. And though there are difficulties scaling this result up to to larger sizes, the material will likely find uses in chip-chip data transfer connections.
A Manchester University  team recently engineered the world's smallest transistor out of graphene: Just one atom deep and ten wide. That scale blows current semiconducting transistors out of the water, and if it extends Moore's law in the same way as has been historically possible, it suggests pocket-sized supercomputers may one day be possible, sipping less power and generating less waste heat than current machines do.
But graphene doesn't just have amazing electrical properties: Mechanical engineers at Columbia University  tested the strength of graphene in a rig that tried to pierce a microscopic sample with a diamond probe. Their discovery suggests that graphene is the strongest material ever found. Though it'd be impossible to use it in this way, if the sample were scaled up to a few inches across it could support the mass of a car on a pinpoint without breaking. On this macroscopic scale, of course, such an atomically-perfect structure would be impossible to maintain, and defects and flaws would weaken the graphene. But it still has potential for incorporation into future super-strong composite materials.
At the University of Crete, graphene is being engineered  into a 3D structure with layers "welded" together with carbon nanotubes, with the intention of creating a next-gen hydrogen fuel tank. It's been found that such a layered material meets the projected mass-storage criteria for holding onto dangerous hydrogen safely in future fuel-cell powered cars: above 6% H2 by mass. Current tech can only manage about 2%.
All this data is coming from Universities for two reasons. First, graphene is incredibly new, and finding out how it behaves is a task for science. Secondly, the wonder material is very hard to manufacture at anything above microscopic scales. The exfoliating "sticky tape" solution suggested above was an early attempt at making graphene, but it could only produce thickish layers. Now much work is being done to prepare it in different ways: by epitaxial growth, or the reduction of silicon carbide, hydrazine or ethanol chemically to produce free-standing "sheets" of graphene.
Presently it's one of the most expensive materials produced on Earth, with a human-hair width sample costing around $1,000 . But there's no reason to believe the problems of large-scale production can't be solved, and create corresponding price slashes.
And with a plethora of diverse applications waiting for it, this carbon material may end up driving on the next industrial revolution. Much as coal drove the first one.