AbstractThe vicinity of the Galactic center harbors many potential accelerators of cosmic rays (CR) that could shine in very-high-energy (VHE) γ-rays, such as pulsar wind nebulae, supernova remnants, binary systems and the central black hole Sgr A*, and is characterized by high gas density, large magnetic fields and a high rate of starburst activity similar to that observed in the core of starburst galaxies. In addition to these astrophysical sources, annihilation of putative WIMPs concentrated in the gravitational well could lead to significant high-energy emission at the Galactic center. The Galactic center region has been observed by atmospheric Cherenkov telescopes, and in particular by the H. E. S. S. array in Namibia for the last ten years above 150 GeV. This large data set, comprising more than 200 hours of observations, led to the discovery of a point-like source spatially compatible with the supermassive black hole Sgr A*, and to an extended diffuse emission, correlated with molecular clouds and attributed to the interaction of cosmic rays with the interstellar medium. Over the same time period, two starburst galaxies, namely M 82 and NGC 253, were detected at TeV energies after very deep exposures. Results from these ten years of observations of the Galactic center region and starburst galaxies at TeV energies are presented, and implications for the various very-high-energy emission mechanisms are discussed.