The Fermilab Muon g −2 experiment recently reported its first measurement of the anomalous magnetic moment aμFNAL, which is in full agreement with the previous BNL measurement and pushes the world average deviation ∆aμ2021 from the Standard Model to a significance of 4.2σ. Here we provide an extensive survey of its impact on beyond the Standard Model physics. We use state-of-the-art calculations and a sophisticated set of tools to make predictions for aμ, dark matter and LHC searches in a wide range of simple models with up to three new fields, that represent some of the few ways that large ∆aμ can be explained. In addition for the particularly well motivated Minimal Supersymmetric Standard Model, we exhaustively cover the scenarios where large ∆aμ can be explained while simultaneously satisfying all relevant data from other experiments. Generally, the aμ result can only be explained by rather small masses and/or large couplings and enhanced chirality flips, which can lead to conflicts with limits from LHC and dark matter experiments. Our results show that the new measurement excludes a large number of models and provides crucial constraints on others. Two-Higgs doublet and leptoquark models provide viable explanations of aμ only in specific versions and in specific parameter ranges. Among all models with up to three fields, only models with chirality enhancements can accommodate aμ and dark matter simultaneously. The MSSM can simultaneously explain aμ and dark matter for Bino-like LSP in several coannihilation regions. Allowing under abundance of the dark matter relic density, the Higgsino- and particularly Wino-like LSP scenarios become promising explanations of the aμ result.