  This article, which is a review with substantial original material, is meant
to offer a comprehensive description of the superfield representations of the
BRST and anti-BRST algebras and their applications to some field-theoretic
topics. After a review of the superfield formalism for gauge theories we
present the same formalism for gerbes and diffeomorphism invariant theories.
The application to diffeomorphisms leads, in particular, to a horizontal
Riemannian geometry in the superspace. We then illustrate the application to
the description of consistent gauge anomalies and Wess-Zumino terms, for which
the formalism seems to be particularly tailor-made. The next subject covered is
the higher spin YM-like theories and their anomalies. Finally, we show that the
BRST superfield formalism applies as well to the N=1 super-YM theories
formulated in the supersymmetric superspace, for the two formalisms go along
with each other very well.
