This thesis gathers a series of observational and phenomenological studies pertaining to compact objects at the center of our Galaxy, i.e. the central supermassive black hole, Sagittarius A, and neutron stars hosted by X-ray bursters. The first part deals with Sgr A, which is subject to daily flares of unknown origins, both from the point of view of the triggers and the radiation mechanisms. This flaring activity has been probed by several extensive multiwavelength campaigns (in gamma-rays, X-rays, infrared and submillimeter) conducted between 2007 and 2009. Data recorded simultaneously by the XMM-Newton/EPIC, INTEGRAL/ISGRI+JEM-X, Fermi/LAT, VLT/NACO+VISIR, and APEX/LABOCA instruments, during new major flares, have helped characterize in detail the spectral and temporal behaviors of these eruptions, and constrain the non-thermal emission models of the radiative medium (synchrotron, inverse Compton, expanding plasmoïd). In a second section, a score of type I X-ray bursts from two transient low-mass X-ray binaries in the Galactic nucleus, GRS 1741.9-2853 and AX J1745.6-2901, have been examined through the data of various low-energy X-ray satellites (2-30 keV). These observations have been discussed in the relatively well established theoretical frame of thermonuclear explosions in a plasma of hydrogen and helium, built up at the surfaces of accreting neutron stars.
