Algebras of supersymmetry protected local and extended operators can provide analytic access to the dynamics of supersymmetric quantum field theories, even when they are strongly interacting. For example, unitary 4d N ≥ 2 superconformal field theories (SCFTs) contain a protected subsector of local operators, the so-called Schur operators, which produce an associated 2d vertex operator algebra (VOA). I will show that one can use these Schur operators to construct a fascinating web of extended operators (lines, surfaces, ...) which exist in every such SCFT. Moreover, these extended operators will mix with the local Schur operators to form a larger algebraic structure called a 2d vertex algebra. I will illustrate the richness of this mixed structure explicitly in the case of a free hypermultiplet.