W-algebras via Lax type operators

W-algebras are certain algebraic structures associated to a finite dimensional Lie algebra and a nilpotent element f via Hamiltonian reduction. In this note we give a review of a recent approach to the study of (classical affine and quantum finite) W-algebras based on the notion of Lax type operators. For a finite dimensional representation of a Lax type operator for W-algebras is constructed using the theory of generalized quasideterminants. This operator carries several pieces of information about the structure and properties of the W-algebras and shows the deep connection of the theory of W-algebras with Yangians and integrable Hamiltonian hierarchies of Lax type equations.