A neutron star binary merges somewhere in the Universe approximately every 10 to 1000 seconds, creating violent explosions potentially observable in gravitational waves and across the electromagnetic spectrum. The observational signatures associated with a binary neutron star merger are intrinsically connected to the fate of the merger remnant. I will discuss the different observational signatures expected in binary neutron star mergers and what kilonovae and short gamma-ray burst observations tell us about the fate of other binary mergers. I will discuss how these observations can shed light onto fundamental questions, such as the behaviour of nuclear matter at supranuclear densities, the jet-launching mechanism of gamma-ray bursts and r-process nucleosynthesis. I will also look to the future, and discuss what we can learn by maximising the value of different messengers in the gravitational-wave multi-messenger era