Abstract:There is compelling evidence that Sgr A*, the extremely compact radio source at the dynamical center of the Galaxy, is associated with a four million solar masses massive black hole. This paper deals with the temporal variability observed in the emission from Sgr A*. The total flux density variation has been puzzling ever since the discovery of Sgr A* in 1974. At radio bands, Sgr A* appears to have significant fluctuations in flux density at shorter centimeter wavelengths and the fractional variation appears to be higher toward the short wavelengths. This trend continues toward higher frequency bands including millimeter, sub-mm, near-infrared and X-ray wavelengths. The observed outbursts exhibit a typical time scale of hours at mm/sub-mm, less than an hour at near-infrared and X-rays. Both Chandra and XMM-Newton X-ray observatories have detected some very strong and highly variable flares from Sgr A*. These observations provide unique constraints on the emission geometry of Sgr A*, and can be use to study the origin of the variability of Sgr A*. Some multi-frequency observations of Sgr A* have detected flares simultaneously at both near-infrared and X-ray bands, and a time delay of the radio flare emission with respect to those at near-infrared and X-rays. These measurements of time delay seem to favor the adiabatically expanding plasmon model. However, more reliable simultaneous multi-frequency campaign is still needed to well establish the relationship between flaring emission at various wavelengths before we can distinguish different theoretical models.