In this paper we provide a first physical interpretation for the Event Horizon Telescope’s (EHT) $2017$ observations of Sgr A$^\ast$. Our main approach is to compare resolved EHT data at $230$GHz and unresolved non-EHT observations from radio to X-ray wavelengths to predictions from a library of models based on time-dependent general relativistic magnetohydrodynamics simulations, including aligned, tilted, and stellar-wind-fed simulations; radiative transfer is performed assuming both thermal and nonthermal electron distribution functions. We test the models against $11$ constraints drawn from EHT $230$ GHz data and observations at $86$ GHz, $2.2$ $\mu\mathrm{m}$, and in the X-ray. All models fail at least one constraint. Light-curve variability provides a particularly severe constraint, failing nearly all strongly magnetized (magnetically arrested disk (MAD)) models and a large fraction of weakly magnetized models. A number of models fail only the variability constraints. We identify a promising cluster of these models, which are MAD and have inclination $i\le 30^\circ$. They have accretion rate $(5.2–9.5) ^\times 10^{-9} M_\odot\mathrm{yr}^{-1}$, bolometric luminosity $(6.8–9.2) \times 10^{35} \mathrm{erg} s^{-1}$, and outflow power $(1.3–4.8) \times 10^{38} \mathrm{erg} s^{-1}$. We also find that all models with $i \ge 70^\circ$ fail at least two constraints, as do all models with equal ion and electron temperature; exploratory, nonthermal model sets tend to have higher $2.2 \mu\mathrm{m}$ flux density; and the population of cold electrons is limited by X-ray constraints due to the risk of bremsstrahlung overproduction. Finally, we discuss physical and numerical limitations of the models, highlighting the possible importance of kinetic effects and duration of the simulations.