The KM3NeT Collaboration is incrementally building a network of water-Cherenkov neutrino observatories in the Mediterranean Sea, consisting of two telescopes, named ARCA (Astroparticle Research with Cosmics in the Abyss) and ORCA (Oscillation Research with
Cosmics in the Abyss), sharing the same detection technology. ARCA, located off the shores of Sicily, in its completed shape will be a cubic-kilometre scale modular telescope made of 230 detection units, optimised for neutrino astronomy in the TeV-PeV energy range. ORCA, off the shores of Toulon (France), will be a 7-Mton modular telescope made of 115 detection units, focused on neutrino oscillations and neutrino mass ordering, for neutrinos in the 1-100 GeV energy range. At the current time, ARCA consists of 21 detection units whereas ORCA has 18 already installed. Both telescopes have been already taking data for a few years, providing good understanding of backgrounds as well as of the expected signals and hence of the scientific
potential of KM3NeT. The technique for neutrino detection and measurement is reviewed, along with outlooks for the completion of the two telescopes and the expected performances for
detection of astrophysical neutrino sources, measurement of neutrino oscillation parameters and neutrino mass ordering. Contributions of KM3NeT to global efforts for multimessenger astronomy are also discussed. Early physics outputs of both telescopes are reported.