[Here][1] are some lectures by Chuck Weibel.  Early on, they discuss Milnor Conjecture and Bloch-Kato, 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.


  [1]: http://www.math.rutgers.edu/~weibel/papers-dir/Bloch-Kato.pdf