  Recently new methods have been introduced to investigate the
non-renormalization properties of the anomalies at a non perturbative level and
in presence of a lattice. The issue is relevant in a number of problems ranging
from the anomaly-free construction of chiral lattice gauge theory with large
cut-off to the universality properties observed in transport coefficients in
condensed matter systems. A review of main results and future perspectives is
presented.
