In physics, the webs of W-algebras are introduced as the vertex algebras associated with the (p, q)-webs of interfaces in the topologically twisted N = 4 super Yang-Mills theory. This class of vertex algebras are generalizations and extensions of the so-called vertex algebras at the corner, or equivalently the affine cosets of hook-type W-algebras in type A. Although not proven yet in general, it has recently been noticed that the webs of W-algebras actually recover the general W-algebras in type A through the ``reduction by stages". In this talk, I will present the first non-trivial examples and some interesting phenomena found in the course both in rational and irrational cases. The talk is based on a joint work with T. Creutzig, J. Fasquel, and A. Linshaw.