The affine W-algebras form an important class of infinite dimensional algebras with applications in integrable systems and geometric representation theory. A special role is played in the theory by W-algebras of "boundary level", in the sense that certain features of the representation theory of W-algebras in general can be determined once the boundary case is understood. I will discuss joint work with T. Arakawa, I. Blatt and W.-B. Yan in which we determine the tensor product structure of boundary W-algebras in type A.