The supermassive black hole (SMBH) at the center of our Milky Way galaxy, Sagittarius A*, is by far the closest such object to us, only about 25 thousand light-years away. Although not nearly as active or luminous as other SMBHs, its relative proximity provides astronomers with a unique opportunity to probe what happens close to the “edge” of a black hole. Monitored in the radio since its discovery and more recently in the infrared and the X-ray, Sgr A* appears to be accreting material at a very low rate, only a few hundredths of an Earth-mass per year. Its X-ray emission is persistent, probably resulting from the rapid motions of electrons in the hot accretion flow associated with the black hole. Once a day there are also flares of emission that are highly variable; they appear more often in the infrared than in X-rays. Some submillimeter wavelength flares have also been tentatively linked to IR flares, although their timing seems to be delayed with respect to infrared events. Despite these intensive observational efforts, the physical mechanisms producing flaring around this SMBH are still unknown and are the topic of intense theoretical modeling.