Neutron-star measurements in the multi-messenger Era

Neutron stars are compact and dense celestial objects that offer the unique opportunity to explore matter and its interactions under conditions that cannot be reproduced elsewhere in the Universe. Their extreme gravitational, rotational and magnetic energy reservoirs fuel the large variety of their emission, which encompasses all available multi-messenger tracers: electromagnetic and gravitational waves, neutrinos, and cosmic rays. However, accurately measuring global neutron-star properties such as mass, radius, and moment of inertia poses significant challenges. Probing internal characteristics such as the crustal composition or superfluid physics is even more complex. This article provides a comprehensive review of the different methods employed to measure neutron-star characteristics and the level of reliance on theoretical models. Understanding these measurement techniques is crucial for advancing our knowledge of neutron-star physics. We also highlight the importance of employing independent methods and adopting a multi-messenger approach to gather complementary data from various observable phenomena as exemplified by the recent breakthroughs in gravitational-wave astronomy and the landmark detection of a binary neutron-star merger. Consolidating the current state of knowledge on neutron-star measurements will enable an accurate interpretation of the current data and errors, and better planning for future observations and experiments.