Wikipedia says:
this circle of ideas is distinct from the Bloch–Kato conjecture of Ktheory, extending the Milnor conjecture, a proof of which was announced in 2009
What exactly is the Ktheory conjecture of BlochKato and has it been proven?
Wikipedia says:
What exactly is the Ktheory conjecture of BlochKato and has it been proven? 


Here are some lectures by Charles Weibel. Early on, they discuss Milnor Conjecture and BlochKato, and they should go through the proof. My understanding is that there were a bunch of people involved in the proof, though a few were a bit reticent to actually write up their parts of it, and so Weibel drew the short straw and is the one writing it up. EDIT: Adding a bit, here's Weibel's 2006 page where he notes the status as of then, and to make sure that this is roughly selfcontained, here's the statement:



Voevodsky gave a talk at a memorial conference for Grothendieck in January 2009 where he announced a full proof of the Bloch Kato Conjecture. The talk is available on google video. 


On 22 June 2013, Joël Riou is going to give a Bourbaki talk on La conjecture de BlochKato [d'après M. Rost et V. Voevodsky].
Usually the notes are put up on http://www.bourbaki.ens.fr/ some time after the actual talk. You can also write to Joël Riou directly at http://www.math.upsud.fr/~riou/. 

