  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
$4.2\sigma$. 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 specific versions and in
specific parameter ranges. Among all models with up to three fields, only
models with chirality enhancements can accommodate $a_\mu$ and dark matter
simultaneously. The MSSM can simultaneously explain $a_\mu$ 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 $a_\mu$ result.
