Long baseline interferometry is now able to resolve the pulsational changes of the angular diameters of a significant number of Cepheids in the solar neighborhood. This allows us to apply a new version of the Baade-Wesselink method to measure their distances, for which we do not need to estimate the star?s temperature. Using this method and angular diameter measurements from the VLT Interferometer, we derived the distances to four nearby Cepheids. For three additional stars, we obtained average values of their angular diameters and we estimated their distances from previously published values of their linear sizes. Based on these new measurements and already existing data, we derived new calibrations of the Period-Luminosity and Period-Radius relations. Additionally, we obtained high precision surface brightness-color relations based solely on interferometric angular diameter measurements on Cepheids and BVRIJHK magnitudes. We finally discuss the prospects of the direct distance measurements of Cepheids.