Neutron stars are gold mines for the study of nuclear systems under extreme conditions of density and isospin asymmetry. Spanning many orders of magnitude in density and pressure, neutron stars display exotic phases that cannot be realised under normal laboratory conditions. Whereas the most common perception of a neutron star is that of a uniform system of neutrons packed to densities that may exceed that of normal nuclei, the reality is far more complex and much more interesting. To illustrate this more exciting reality, the editors of this book contacted leaders in the field of neutron-star physics with expertise ranging from nuclear structure to stellar dynamics. They asked each expert to communicate the successes of the past and the challenges of the future in a way that will continue to foster dialogue and promote collaborations between the astrophysics and the nuclear physics communities.