Diamond jubilee symposium on pulsars,14-17 March 1994, RRI, Bangalore.Observational evidence, and theoretical models of the magnetic field evolution of neutron stars is discussed. Observational data indicates that the magnetic field of a neutron star decays significantly only if it has been a member of a close interacting binary. Theoretically, the magnetic field evolution has been related to the processing of a neutron star in a binary system through the spin evolution of the neutron star, and also through the accretion of matter on the neutron star surface. I describe two specific models, one in which magnetic flux is expelled from the superconducting core during spin-down, via a copuling between Abrikosov fluxoids and Onsager-Feynman vor...