Neutron stars are still almost as mysterious as during the moment of their observational discovery more than 50 years ago. Today however we are equipped in a set of modern observational tools that help us uncover their secrets, closely related to the state of the densest matter existing in the Universe. In this talk I will present our knowledge of neutron stars, as we understand them thanks to observations in various electromagnetic domains and in gravitational waves, and discuss the prospects of the multi-messenger observations in the future.