The EGRET instrument on the Compton Gamma- Ray Observatory has observed the Galactic Center (GC) region with good coverage at a number of epochs. A strong excess of emission is observed, peaking at energies > 500 MeV in an error circle of 0.2 degree radius including the position l =0 and b =0 . The close coincidence of this excess with the GC direction and the fact that it is the strongest emission maximum within 15 degrees from the GC is taken as compelling evidence for the source's location in the GC region. The history of the emission intensity, observed over 5 years, leaves room for pos- sible time variation; however, it does not provide evidence. The angular extent of the excess appears only marginally compati- ble with the signature expected for a single compact object. The emission therefore may stem from one or more compact objects or may originate from diffuse interactions within 85 pc from the center of the Galaxy at 8.5 kpc distance. The spatial distri- bution of the emission does not correlate with the details of the CO-line surveys. Thus, in spite of the existence of a strong emis- sion peak, earlier conclusions based on an apparent 'gamma-ray deficit', postulating the masses of the 'wide-line' clouds in the GC area to be an order of magnitude lower than indicated by naive CO interpretation, are supported. However, the total gas mass in the Nuclear Bulge (NB) derived from the gamma-ray emission is found to be in agreement with the mass which in recent studies has been derived from molecular-line and FIR surveys. The -ray emission spectrum is peculiar and different from the spectrum of the large-scale galactic diffuse emission. A diffuse emission scenario requires an enhanced and peculiar Cosmic Ray (CR) spectrum as suggested for the electrons in the 'Radio Arc'. A compact sources model hints at an origin in pulsars. While the spectrum suggests middle-aged pulsars like Vela, too many are required to produce the observed flux.