Invitation to higher local fields, Part I, section 15: On the structure   of the Milnor K-groups of complete discrete valuation fields
  This work contains a list of all known results on the quotient filtration on the Milnor K-groups of a complete discrete valuation field in terms of differential modules over the residue field . Author's recent study of the case of a tamely ramified field of characteristic 0 with residue field of characteristic p by using an exponential map and a syntomic complex is explained. 
Jinya Nakamura