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 Roentgen Satellite (ROSAT) results to narrow its range to 0.5-1 x 10(exp 23)/sq cm. 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 solar mass and in 1E 1740.7-2942 to be less than 9 solar mass. 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 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 possible physical mechanisms responsible for producing both the long-term X-ray variations and the radio jets are postulated. We also 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.
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