In this paper we discuss a variety of issues concerning the exciting and mysterious Galactic center gamma-ray sources 1E 1740.7-2942 and GRS 1758-258. We discuss the problem associated with the highly uncertain X-ray absorption column toward 1E 1740.7-2942 and use the recent ROSAT results to narrow its range to 0.5-1 X 10(3) cm-2. Then the current upper limits from deep optical and near-IR searches of stellar objects at these source locations are plotted on an H-R diagram, from which we find the mass of a potential companion star of the (supposed) black hole in GRS 1758-258 to be less than 4 M. and in 1E 1740.7-2942 to be less than 9 M. The observed well-collimated radio jets in 1E 1740.7 - 2942 require the existence of a stable accretion disk (presumably from binary accretion). The apparent association of 1E 1740.7-2942 with a high-density molecular cloud, on the other hand, points to possible accretion directly from the interstellar medium (ISM). We present an analysis of the energetics and kinematics of the radio jets in 1E 1740.7 - 2942. We find that the jets of 1E 1740.7-2942 are most probably made of normal proton-electron plasma (<20%) and electron-positron pairs. The observed good alignment of the radio core with its lobes implies that the source is moving in the ISM slowly (< 10 km s-1). We present the long-term X-ray light curves of the two sources which include both the Granat/SIGMA's 3 yr monitoring data and all the data from previous imaging balloon and satellite observations over the last decade. The large amplitude, nonperiodic hard X-ray variabilities of these two sources appear to be similar, which suggest a common origin. The possible physical mechanisms responsible for producing both the long-term X-ray variations and the radio jets are postulated. Since the optical/near-IR and radio observations have excluded these systems as high-mass X-ray binaries like Cyg X-1 which accrete from strong stellar winds of massive companions, we consider Roche lobe-overflowing, low-mass X-ray binaries and Bondi-Hoyle accretion directly from a high-density surrounding medium. We propose a plausible scenario in which both sources are binary systems with a black hole primary and a low-mass companion and they are accreting mainly from the ISM at a rate self-regulated by the interaction between the accretion flow and the emerging hard X-ray flux.