We are entering an era of unprecedented capabilities for astronomical observations. The analysis of signals in multiple bands, i.e., gravitational waves, neutrino, gamma and X-rays emissions, will provide detailed insight about the physics of diverse astrophysical phenomena. In particular, neutron-star mergers represent one of the most interesting sources for these multi-messenger signals. The evolution of a merger is closely linked to gravity, nuclear and neutrino physics. Thus,observing such mergers promises answers to many unresolved puzzles, among others: Where and how are elements like gold produced in our Universe? What is the mechanism of powerful stellar explosions? In this colloquium, I shall provide an overview of neutron stars, as well as mergers and accretion disks in the context of nuclear astrophysics. I will discuss their connection to properties of nuclear matter and neutrino physics, presenting results on gravitational wave signals, neutrino observation, and the synthesis of neutron-rich nuclei.