Abstract: The concept of neutron stars (NSs) comes as a natural inference from our understanding of the fundamental structure of matter, and is an indispensable part of stellar evolution theory. Since the discovery of pulsars in 1967 that confirmed the existence of NSs, people have observed thousands of NSs of various types, and from multi-wavelength and multi-messenger observations have probed their electromagnetic radiation mechanism, the interaction between NSs and their binary companions, the gravitational wave radiation from double NSs, and so forth. The mysterious internal constituents of NSs and their equation of state, the most fundamental problems in NS research, have also been constrained observationally through several different methods.