Conformal covariance in 2d conformal and integrable models, in W-algebras and in their supersymmetric extensions

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.