Finding exoearths, rocky planets orbiting other Suns, is one of the boldest objectives of present day astrophysics. This quest is motivating the development of new ground and space based facilities led by the major international agencies. One of these is the ESPRESSO spectrograph, operating since 2018 at ESO’s VLT telescopes. ESPRESSO offers the potential to detect and characterise earth-mass planets orbiting other suns, as well as the possibility to study exoplanet atmospheres in unique detail.

In this talk I will start by briefly presenting the major efforts to detect and characterise rocky planets orbiting other stars. I will then focus on ESPRESSO and on its major results in the quest for Earth-like worlds. Finally, I will discuss one of the major difficulties that presently challenge these quests: the stellar noise. A novel approach to this problem will be presented.