Haven't researched voxels thoroughly, so take my explanation worth a grain of salt. But essentially voxels (derived from virtual pixels) are pixels dispersed in 3D space. Entirely different concept from anything polygonal. Think more like, particles. If you zoom close enough into a stream of particle effects like smoke or something, you can't see through either, right? If you look at a "lo res" voxel model, you can see the jagged individual voxels. But since you can render many more of them less "expensively" than polygons, you can use enough to make your models as smooth as you'd like.

What's the downsides to it? I know Novalogic used to use it for large, open areas with not much in terms of stuff, so possibly it's bad for urban scenery or something like that?

I have no idea what is going on in this thread, but i like the word "Voxels".
So, uhm, yay voxels!

But doesn't Crysis use Voxels? That looked pretty.

Just for the terrain though. Which further builds on my argument it's only good for large areas and expanses.

Its a variation of the well known voxels, I would say that they still are plain voxels. The difference to "past voxel renderers" is that they had the voxels in a 3-Dimensional matrix.
This appears to be a hierarchical model, kinda like specifying your location with continent-country-city-street instead of direct coordinates - eg. if you take a snapshot in France you dont need to check if Americans are in the picture. Thats nothing new and many (I suspect most) polygon game already use such approaches to skip rendering non-visible polygons.
Its similar to saying you invented an algorithm that only visible pixel-sized polygons are rendered. Its similar bullshit as this hierarchical structures get very complicated (and less efficient) if those are dynamic - like having animation or moving parts. If they really have developed a perfect algorithm it would be easy to make it work exactly the same way with polygons, and polygons have alot of advantages as getting surface-normals (used for lighting and collision physics) is easy and fine surface detail can be easy and efficiently added via textures and shaders.
And "Infinite geometry"? Trying desperatly to grab dumb investors?

They, just like Outcast before them, use poligons on top of those voxels to do reflection calculations.

Actually, you're correct on all accounts. That's how it works, you can even see the points get bigger than a pixel and start to look jagged when they get too close. The idea is to have enough points that it doesn't matter, but then it takes up a shitload of space. I don't know about memory, they seem to be doing something unique with their algorithm in that regard.
You have to rethink everything about graphics though. People have been asking about textures, but that sort of thing doesn't even apply anymore. Each point now contains its own color and textures are actually geometric.

It made me think of metaballs at first. Infinite number of points for very little storage space. That doesn't seem to be what they're doing though. For one thing, the palm leaves in some of the screenshots would be ridiculously hard to model in metaballs.
The whole thing smells. They don't even give a paper napkin explanation of how it works. Sorting? Only drawing what's on the screen? So did Quake ( + [url=http://en.wikipedia.org/wiki/Potentially_visible_set]PVS) but it definitely didn't have infinite geometry.
It's like explaining how a perpetual motion machine works by saying "well, it just keeps spinning, no matter what." Thanks, that's helpful.

With buttered bread strapped to the back of a cat, duh.

Um, useless post?
Voxels were used in Alpha Centauri I think for the graphics. That game didn't take off either though it rocked, unlike voxels which offer no real benefit but a ton of deficits. Can't list them all, but voxels were phased out for a reason and that was they were not as good as the polygon.

Do you have one in your basement?

Hexplore used voxels.

Just found this interview with John Carmack. He describes something that sounds like it may be similar.
So the tech is legitimate, they just present it in a completely obtuse manner (lots of hyperbole with no technical details).