The best starting point might be Weibel’s attempt to structure and survey the whole proof, and his list of references. See his webpage, or notes from some talk og his.
Let be a field, and an integer, prime to . Then the Galois symbol \\theta: K^M_q(F) / n \\to H^p_{Gal}(F, \\mu_n^{\\otimes q}) is an isomorphism.
For background on many ideas, see Gille and Szamuely, in Various folder under ALGEBRA
Voevodsky and Suslin: Bloch-Kato conj and motivic cohom with finite coeffs, file in Voevodsky folder
Voevodsky: BK conjecture for Z mod 2 coeffs and algebraic Morava K-theories. File in Voevodsky folder. Discussion of BK conj and related conjectures. P 32: axioms for cohomology theories on simplicial schemes. Proof that existence of algebraic Morava K-theories satisfying certain properties would imply the BK conjecture.
Weibel on some axioms related to the Voevodsky-Rost program: http://www.math.uiuc.edu/K-theory/0809
Some special case, by Koya, and another special case
Something by Levine and Geisser
An ingredient on norm varieties
The Gersten conjecture for Milnor K-theory , by Moritz Kerz
Papers involved in BK proof, from Weibel talk: Weibel , J Top 2009, pp346 V: Eilenberg-M spaces V: Motivic cohom with Z/2 coeffs IHES 2003 V: Reduced power ops (not refereed/published) Suslin-Joukhovitsky JPAA 206. Haesemeyer-W: Chain lemma etc after Rost, Oslo Symposium 2009 Rost: Chain lemma etc, on his website V: Simplicial radditive functors, AKA Delta-closed classes V: Motives over simplicial schemes V: Motivic cohom with Z/l coeffs (2003, 2008) S-V: Bloch-Kato paper 2001 Also Geisser-Levine Suslin: Grayson ss
nLab page on Bloch-Kato conjecture