Two decades have passed since the initial proposition that amyloids are not only (toxic) byproducts of an unintended aggregation cascade, but that they can also be produced by an organism to serve a defined biological function. That revolutionary idea was borne out of the realization that a large fraction of the extracellular matrix that holds Gram-negative cells into a persistent biofilm is composed of protein fibers (curli; tafi) with cross-β architecture, nucleation-dependent polymerization kinetics and classic amyloid tinctorial properties. The list of proteins shown to form so-called functional amyloid fibers in vivo has greatly expanded over the years, but detailed structural insights have not followed at a similar pace in part due to the associated experimental barriers. Here we combine extensive AlphaFold2 modelling and cryo-electron transmission microscopy to propose an atomic model of curli protofibrils, and their higher modes of organization. We uncover an unexpected structural diversity of curli building blocks and fibril architectures. Our results allow for a rationalization of the extreme physico-chemical robustness of curli, as well as earlier observations of inter-species curli promiscuity, and should facilitate further engineering efforts to expand the repertoire of curli-based functional materials.