Hypergraph categories are monoidal categories in which every object is equipped with a special commutative Frobenius monoid. Morphisms in a hypergraph category can hence be represented by string diagrams in which strings can branch and split: diagrams that are reminiscent of electrical circuit diagrams. As such they provide a framework for formalising the syntax and semantics of circuit-type diagrammatic languages. In this talk I will introduce decorated corelations as a tool for building hypergraph categories and hypergraph functors, drawing examples from linear algebra and dynamical systems.