We use representation theory of quantum toroidal algebras to give a uniform construction of all known deformations of W algebras corresponding to Dynkin diagrams of classical types. Moreover, our method produces a number of new examples, covering, in particular, supersymmetric cases. It allows us to construct analogs of local integrals of motions in all cases. We discuss the existence of the affine screening operator commuting with the integrals of motion. The affine screening operators correspond to deformations of affine Cartan matrices of classical types (twisted, untwisted, and supersymmetric). This is a joint work with B. Feigin, M. Jimbo, and I. Vilkoviskiy.