Oral title: Solar system analogs around solar twins Oral abstract: Solar twins are solar mass (1.00+/-0.05 M_Sol) and solar metallicity (-0.1 < [Fe/H] < +0.1) main sequence stars; therefore they are key to study the past and future evolution of the Sun and its planetary system. Our Solar Twin Planet Search with HARPS/ESO has been monitoring 66 solar twins for planets, having already more than seven years of observations, considering also archive data. The most promising solar system analog from our survey is HIP 11915, a solar-age solar twin with a Jupiter twin, a giant planet with the same mass as Jupiter (0.99 M_Jup) and located at 4.8 AU (compared to 5.2 AU for Jupiter in our solar system). No further planets have been found in the inner region, but the similar chemistry (depletion of rocky-forming material) between HIP 11915 and the Sun, opens the possibility of terrestrial planets in HIP 11915. We have recently found another Jupiter analog; hence there are at least 3% of potential solar system analogs in our sample. Finally, from a recent high precision (0.01 dex) abundance study of the largest sample of solar twins, we have found that the Sun has a subtle deficiency of rocky material relative to 94% of solar twins, arguing for a relatively small fraction of true solar system analogs.