  A cohomological BRST characterization of the Seiberg-Witten (SW) map is
given. We prove that the coefficients of the SW map can be identified with
elements of the cohomology of the BRST operator modulo a total derivative. As
an example, it will be illustrated how the first coefficients of the SW map can
be written in terms of the Chern-Simons three form. This suggests a deep
topological and geometrical origin of the SW map. The existence of the map for
both Abelian and non-Abelian case is discussed. By using a recursive argument
and the associativity of the $\star$-product, we shall be able to prove that
the Wess-Zumino consistency condition for non-commutative BRST transformations
is fulfilled. The recipe of obtaining an explicit solution by use of the
homotopy operator is briefly reviewed in the Abelian case.
