The X-ray emission from Sgr A^* is rather weak in quiescence with Lx  0.5 L_ּ in the Chandra band of 2–10 keV. However, Sgr A^* has been observed to flare at least once for a few hours, reaching a peak luminosity of > 25 L_ּ (Baganoff et al 2001a). The flare had a distinctively harder spectrum, with the spectral index α changing from 1.2 to 0.3 (L_ν ∝ ν^−α). The spectral index, variability, and flux of both states place significant constraints on Sgr A^* accretion models. For example, the quiescent spectral index is probably too soft to be due to thermal bremsstrahlung emission alone (Liu and Melia 2002); it is more likely due to Comptonization of the radio synchrotron photons (SSC). On the other hand, it is not clear whether the flare emission is due to thermal bremsstrahlung (Liu and Melia 2002) or SSC (Falcke and Markoff 2000). In any case, significant SSC only occurs if the peak electron temperature > 10¹⁰ K, a temperature ADAF models do not reach. A possible solution to this is a combination ADAF plus jet model, which reproduces the observed spectral indices and fluxes of both states rather well (Markoff et al 2001). Future simultaneous multi-wavelength observations should determine whether thermal bremsstrahlung, which is extended and mostly decoupled from the radio emission, or SSC, which is directly tied to the sub-mm emission, is dominant for Sgr A^*.