  Conformal symmetry underlies the mathematical description of various
two-dimensional integrable models (e.g. for their Lax representation, Poisson
algebra, zero curvature representation,...) or of conformal models (for the
anomalous Ward identities, operator product expansion, Krichever-Novikov
algebra,...) and of W-algebras. Here, we review the construction of conformally
covariant differential operators which allow to render the conformal covariance
manifest. The N=1 and N=2 supersymmetric generalizations of these results are
also indicated and it is shown that they involve nonstandard matrix formats of
Lie superalgebras.
