Since the discovery in 1995 of 51 Peg b, radial velocity searches have proven to be one of the most effective ways of finding new extrasolar planets, in particular extrasolar planets orbiting nearby stars, where transits are often not detected. Back when the first exoplanet orbiting a Sun-like star was discovered, it was possible to detect the presence of a Jupiter-like planet in a close orbit to its star. Today, high-precision radial velocity measurements, obtained using high-resolution spectrographs, allow us to find Earth-mass planets that orbit inside, or close to, the habitable zone of their host stars. In some cases, with new-generation instruments such as ESPRESSO, it is possible to detect the presence of planets much lighter than the Earth. At these levels of precision, signals induced by stellar activity in the RV curves become the most important limiting factor, even in the case of magnetically quiet stars. Stellar activity can induce apparent Doppler shifts of the stellar spectrum, which cause periodic signals that range from less than one to dozens of meters per second. The correct detection and characterization of the different star-induced signals and their effect in the RVs is one of the most important steps to detect and properly characterize low-mass exoplanets, and its importance increases with increased precision as, even in the case of the quietest stars, these activity-induced signals can be the dominant signals in the data. Here, will embark in a short journey on the history of the radial velocity technique as a mean to detect extrasolar planets. From the early concept of spectrographs dedicated to the measurement of stellar velocities, to the detection of a planet with 1/4 the mass of the Earth orbiting Proxima Centauri.