The ZX calculus, its many variants and closely related calculi are by now established tools in the quantum community, being used by practitioners to optimise quantum circuits, improve error correction algorithms etc. At its core, the calculus features an interaction of two algebraic structures: Hopf algebra and Frobenius algebra. While faithfully describing the category of Hilbert spaces with the tensor product, the same two algebraic structures describe traditional linear algebra – or more accurately, the category of linear relations with, instead of the usual tensor product, the direct sum. More generally, Frobenius algebra seems to be at the core of relational reasoning, playing a fundamental role in relational accounts of regular logic (cartesian bicategories) and even full first order logic (first order bicategories). In this talk I will survey recent work in this area.