Neutron stars are dense, compact objects that offer unique insights into matter under extreme conditions. They emit various signals, including electromagnetic waves, gravitational waves, neutrinos, and cosmic rays, making them key targets for multi-messenger astronomy. However, accurately measuring their properties like mass, radius, and moment of inertia is challenging due to indirect observables and model dependencies. This review discusses methods for measuring neutron-star characteristics, emphasizing the importance of independent techniques and multi-messenger approaches. It highlights the role of gravitational waves in constraining neutron-star physics, as demonstrated by the detection of binary neutron-star mergers. The review covers various methods, including binary mass functions, Shapiro delay, gravitational-wave asteroseismology, and observations of magnetic fields and crustal physics. It also discusses the importance of understanding neutron-star structure and composition, and how measurements of these properties can help constrain the equation of state of dense matter. The review concludes that combining different measurement techniques and multi-messenger data is crucial for advancing our understanding of neutron-star physics.Neutron stars are dense, compact objects that offer unique insights into matter under extreme conditions. They emit various signals, including electromagnetic waves, gravitational waves, neutrinos, and cosmic rays, making them key targets for multi-messenger astronomy. However, accurately measuring their properties like mass, radius, and moment of inertia is challenging due to indirect observables and model dependencies. This review discusses methods for measuring neutron-star characteristics, emphasizing the importance of independent techniques and multi-messenger approaches. It highlights the role of gravitational waves in constraining neutron-star physics, as demonstrated by the detection of binary neutron-star mergers. The review covers various methods, including binary mass functions, Shapiro delay, gravitational-wave asteroseismology, and observations of magnetic fields and crustal physics. It also discusses the importance of understanding neutron-star structure and composition, and how measurements of these properties can help constrain the equation of state of dense matter. The review concludes that combining different measurement techniques and multi-messenger data is crucial for advancing our understanding of neutron-star physics.