  We revisit quantum field theory anomalies, emphasizing the interplay with
diffeomorphisms and supersymmetry. The Ward identities of the latter induce
Noether currents of all continuous symmetries, and we point out how these
consistent currents are replaced by their covariant form through the appearance
of the Bardeen-Zumino currents, which play a central role in our study. For
supersymmetry Ward identities, two systematic methods for solving the
Wess-Zumino consistency conditions are discussed: anomaly inflow and anomaly
descent. The simplest inflows are from supersymmetric Chern-Simons actions in
one dimension higher, which are used to supersymmetrize flavor anomalies in
$d=4$ and, for $d=2$ $\mathcal{N}=(p,q)$, flavor anomalies with $p,q\leq 3$ and
Lorentz-Weyl anomalies with $p,q\leq 6$. Finally, we extend the BRST algebra
and the subsequent descent, a necessity for the diffeomorphism anomaly in
retrospect. The same modification computes the supersymmetrized anomalies, and
determines the above Chern-Simons actions when these exist.
