Over the past two decades, Vertex Operator Algebras (VOA) have appeared in various contexts in gauge theory. I will discuss a class of VOAs arising as algebras of local operators at junctions of interfaces in four-dimensional N=4 super Yang-Mills theory. The simplest trivalent junction leads to a three-parameter family of algebras $Y_{L,M,N}$ generalizing famous $W_N$ algebras playing an important role in the AGT correspondence. Gluing trivalent junctions into a more complicated webs of interfaces can be lifted to gluing VOAs establishing a pictorial way to construct and study VOAs. At the level of characters, the gluing construction agrees with the topological-vertex-like counting of D4-D2-D0 branes in toric Calabi-Yau three-folds. A dual perspective in terms of M5-branes mutually intersecting in toric Calabi-Yau three-folds suggests a generalization of the AGT correspondence for such "spiked instanton" configurations.