Gravitational-wave observations  have recently opened new perspectives in the multi-messenger observations of the most energetic events in the Universe. Starting from recent observations of the Advanced Virgo and LIGO detectors and the current electromagnetic (EM) observatories, the talk will give an overview of the innovative observational resources expected in the next decade. The third generation of GW observatories, such as Einstein Telescope and Cosmic Explorer will allow us for the first time to observe GWs along cosmic history back to the cosmological dark ages. They will operate in synergy with a new generation of EM observatories, such as CTA, Athena, the Vera Rubin Observatory, JWST, ELT, SKA and the mission concepts THESEUS and HERMES. This network will probe the formation, evolution and physics of binary systems of compact objects in connection with kilonovae and short gamma-ray bursts along with the star formation history and chemical evolution of the Universe. The talk will focus on multi-messenger challenges and perspectives in astrophysics.