The magnetic fields of young neutron stars are the most intense known to humankind, exceeding those achievable on the Earth by perhaps six orders of magnitude. It is these magnetic fields which make neutron stars observable as radio pulsars. In this paper we discuss what we know about these fields and how they evolve with time. The fields of the oldest pulsars, the millisecond pulsars, are much smaller and appear to be reduced during the process of accretion which is responsible for their rapid rotation rates. The pulsed nature of the radiation from pulsars also makes them excellent probes of the very weak field of the interstellar medium and we briefly describe what we have learned about these fields, which are perhaps 20 orders of magnitude smaller than the fields in the neutron stars themselves.