We present results from the first two years of operations of the HARPS spectrograph installed on the ESO 3.6m telescope at La Silla Observatory, Chile. This instrument, primarily built to detect extrasolar planetary systems, was designed to achieve the highest radial velocity precision ever, thanks to high mechanical and environmental stability, stable illumination, accurate wavelength calibration and tracking of instrumental drifts. HARPS has demonstrated a long-term accuracy at the 1 m s-1 level and below, exploring a new regime in RV precision. We present recent improvements in the wavelength calibration process, including the creation of a new ThAr reference atlas and the use of a much larger number of lines to fit the wavelength solution. We have also investigated the intrinsic stability of ThAr calibration lamps and show that they are able to provide a long-term wavelength reference at or below the 1 m s-1 level. Other instrumental error sources such as guiding accuracy and photon noise are discussed and a global error budget is presented. These efforts to further improve the RV precision are also part of a broader study to build a ultra-high accuracy spectrovelocimeter for the ESO OWL telescope, the CODEX project. The aim of this instrument is to reach an accuracy of 1 cm s-1 over timescales of at least ten years. This requires to push down the limits of present-day calibration techniques and to explore new technologies able to provide ultra-precise Doppler measurements.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.