After having found hundreds of extra-solar planets, the radial-velocity (RV) technique starts to be limited by intrinsic stellar signals. Indeed, at the level of the best spectrographs, one starts to see the effects induced by stellar pressure waves, convection, surface activity coupled with stellar rotation, and magnetic cycles. The questions of how to extract and analyse the different stellar signals from RV data, and how to mitigate their contributions have been studied in detail. In addition, optimizing the observational strategy to look for planets can also help in mitigating short-term stellar signal effects. As a result, a few dozen of the lowest mass planets known so far have been discovered following the work performed in this thesis. Among these planets, we have discovered Alpha Centauri Bb, the lightest extra-solar planet detected so far with the RV technique, and the closest one to our Solar System.