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Tens of Zr inter-atomic potentials (force fields) have been developed to enable atomic-scale simulations of Zr alloys. These can provide critical insight in the in-reactor behaviour of nuclear fuel cladding and structural components exposed, but the results are strongly sensitive to the choice of potential. We provide a comprehensive comparison of 13 popular Zr potentials, and assess their ability to reproduce key physical, mechanical, structural and thermodynamic properties of Zr. We assess the lattice parameters, thermal expansion, melting point, volume-energy response, allotropic phase stability, elastic properties, and point defect energies, and compare them to experimental and ab-initio values. No potential was found to outperform all others on all aspects, but for every metric considered here, at least one potential was found to provide reliable results. Older embedded-atom method (EAM) potentials tend to excel in 2-3 metrics each, but at the cost of poorer transferability. The two highest-performing potentials overall, with complementary strengths and weaknesses, were the 2021 angular-dependent potential of Smirnova and Starikov (Comp. Mater. Sci. 197, 110581) and the 2019 embedded-atom method potential of Wimmer et al (J. Nucl. Mater. 532, 152055). All potentials trained through machine learning algorithms proved to have lower overall accuracy, and less transferability, than simpler and computationally faster potentials available. Point defect structures and energies is where the greatest divergence and least accuracy is observed. We created maps that will help modellers select the most suitable potential for a specific application, and which may help identify areas of improvement in future potentials., 32 pages, 11 Figures