High-resolution, high-stability spectroscopy is crucial for the precise determination of radial velocities and the detailed chemical analysis of stars in different contexts of the Galaxy. The ESPRESSO and HORuS spectrographs, in operation on the VLT and GTC telescopes since mid-2018, are already contributing significantly to our knowledge of exoplanets and the early stages of the Milky Way. ESPRESSO, whose science team we are part of, will allow us to detect planets similar to Earth in the stars closest to the Sun and characterize their masses and atmospheres. Some of these exo-Earths will be in their habitable zones, and therefore will be targets for the study of their atmospheres with the next generation of instruments, such as HIRES at the ELT, whose instrumental development we are involved in, coordinating the Spanish contribution to HIRES. NIRPS is an ultra-stable infrared spectrograph that will work together with HARPS at ESO's 3.6m telescope, for the detection and characterization of planets around red dwarf stars. HORuS will allow us to investigate the chemistry of metal-poor stars in the halo of the Milky Way, identified from spectra from large databases such as DESI and WEAVE, whose science teams we are part of. The composition of the atmospheres of these stars provides information about the first generation of stars of zero metallicity that formed after the "Big Bang", the chemical enrichment that took place during the formation of the Galaxy and the nucleosynthesis in the first stars and their supernovae.