i will explain the cohomological approach to local class field theory, and how it generalizes to higher local fields. for example, a 2-local field k is a complete discrete valuation field with residue field a local field; class field theory for k states, in part, that there is an artin map from $k_2(k)$ to the abelianized absolute galois group of k. i will show how the cohomological approach can be used to construct a weil group for any finite extension of 2-local fields.