Observations of Sgr A* over the past 4 years with the Keck Telescope in the near-infrared, coupled with millimeter and submillimeter observations, show that the 3.7×106M⊙ Galactic Black Hole, Sagittarius A*, displays continuous variability at all these wavelengths, with the variability power concentrated on characteristic time scales of a few hours, and with a variability fraction that increases with wavelength. We review the observations indicating that the few-hour time scale for variability is reproduced at all accessible wavelengths. Interpreted as a dynamical time, this time scale corresponds to a radial distance of 2 AU, or ∼25 Schwarzschild radii. Searches for quasi-periodicities in the near-infrared data from the Keck Telescope have so far been negative. One interpretation of the character of these variations is that they result from a recurring disk instability, rather than from variations in the mass accretion rate flowing through the outer boundary of the emission region. However, neither a variable accretion rate nor a mechanism associated with a jet can presently be ruled out.