Well, the field bet won this year - no one had Daniel Schechtman and quasicrystals in their predictions, as far as I know. This is one of those prizes that is not easy to communicate to someone outside the field, but if I had to sum it up in one phrase for a nonscientist, it would be "Discovery of crystals that everyone thought were impossible".
That's because they have five-fold symmetry, among other types. And the problem there is pretty easy to show: if you take a bunch of identical triangles (any triangle at all), you can tile them out and cover a surface evenly - imagine a tabletop mosaic or a bathroom floor. And that works with any rectangle, too, naturally, and it also works with hexagons. But it does not work with regular pentagons (or with any other regular geometric figure). Gaps appear that cannot be closed. You can cheat and tile the plane with two types of bent pentagons or the like, but closer inspection shows that these cases are all really tiles of one of the allowed classes.
The same problems appear in three-dimensional crystals, and five-fold symmetry, in any of its forms, is just not allowed (and had never been seen). But in the early 1980s there came a report of just that. Daniel Schechtman, working at the National Bureau of Standards, had found a metallic crystalline substance that seemed to show clear evidence of an impossible form. I was in grad school when the result came out, and I well remember the stir it caused. Just publishing the result took a lot of nerve, since every single crystallographer in the world would tell you that if they knew one thing about their field, it was that you couldn't have something like this.
As it turned out, these issues had already been well explored by two different groups: medieval Islamic artists and mathematicians. It turns out that what looks like unallowable symmetry in two (or three) dimensions works out just fine in higher-dimensional spaces, and these theoretical underpinnings were actually a lot of help in the debates that followed.
Here's a good history of what happened afterwards. One thing that I recalled was that Linus Pauling wasn't buying it for a minute. He was, of course, quite old by that time, but he was still a force to be reckoned with in his own areas of expertise, despite the damage he'd done to his reputation with all the Vitamin C business. He kept up the barrage for the remainder of his life, publishing one of his last scientific papers (in 1992) on the subject and arguing yet again that the quasicrystal idea was mistaken. As that above-linked paper from Schechtman's co-worker John Cahn put it:
Quasicrystals provided win-win opportunities for crystallographers: If we were mistaken about them, expert crystallographers could debunk us; if we were right, here was an opportunity to be a trail blazer. While many crystallographers worldwide availed themselves of the opportunity, U.S. crystallographers avoided it, to a large extent because of Pauling’s influence.
But time has shown that the quasicrystal hypothesis is correct. You can have local symmetries of this kind, and many other "impossible" examples have been discovered since. The resolution of the X-ray structures has gotten better and better, ruling out all the other explanations - Pauling would have found it painful to watch. The resulting solids have rather odd properties, although if someone asked me to name any effect that they've had on anyone's daily life, I'd have to answer "none at all". But I'm sympathetic to anyone who proves something in science that no one thought could be proved, so Nobel Prize it is, and congratulations.
A side note: anyone want to take bets on whether some ayatollah or other Iranian politician will pop up, claiming that the whole subject of the prize was anticipated by the 15th-century Darb-e Imam shrine in Isfahan? Let's set the odds. . .