Since 2005, researchers at the Brain and Mind Institute of the École Polytechnique have been working on reverse-engineering a small piece of rat brains. This small piece is called a cortical column, and it's made up of an intricate network of some 10,000 individual neurons, each one of which requires about as much computer power as your average laptop to model. Put 100,000 of these columns together and you've got a model of a fully-functional rat brain.
So that's all well and good if you're a rat, but if you're a human looking for a new brain, you're going to need something a little more complicated. Think 100,000 individual neurons per cortical column and maybe two million columns, which is some really big number of neurons that's going to require a correspondingly big number of computer processors to accurately replicate.
To make this happen, Blue Brain Project is hoping for 100 million euros a year for the next ten years to build a ludicrously large and powerful brain-modeling computer. And when they're done with it, they hope to use it to figure out why our brains do some of the weird stuff that they do, ranging from neurological disorders to consciousness.
Check out a gallery of some pics of the project, and for more info, you can watch a TED Talk about it here.