New physics explanations of $a_mu$ in light of the FNAL muon $g-2$ measurement

The Fermilab Muon $g-2$ experiment recently reported its first measurement of the anomalous magnetic moment $a_mu^{textrm{FNAL}}$, which is in full agreement with the previous BNL measurement and pushes the world average deviation $Delta a_mu^{2021}$ from the Standard Model to a significance of $4.2sigma$. 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 $a_mu$, 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 $Delta a_mu$ can be explained. In addition for the particularly well motivated Minimal Supersymmetric Standard Model, we exhaustively cover the scenarios where large $Delta a_mu$ can be explained while simultaneously satisfying all relevant data from other experiments. Generally, the $Delta a_mu$ 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 $a_mu$ only in specif