Results and new progress of the origin and evolution of pulsar magnetic fields are reviewed. Lots of models about how such strong magnetic fields were generated, mainly two kinds of structures were proposed for initial magnetic fields: fields confined in the cores and fields confined in the crusts of neutron stars. No consensus has been reached on whether the magnetic fields decay or not, despite some observational evidence for the evolution of magnetic fields. The discrepancy between characteristic ages and kinematics ages indicates that the magnetic fields decay exponentially. On the other hand, the braking indices of several young pulsars and the comparison between pulsar characteristic ages and the ages of associated supernova remnants suggest that the magnetic fields of young pulsars grow like a power-law. Pulsar population synthesis is one of the most important methods to investigate the evolution of magnetic fields. Many simulations show that if magnetic fields do decay exponentially, the e-folding decay time should be 100 Myr or longer. The numerical calculations of the Ohmic decay in the crust indicate that the scenario of exponential decay is oversimple, and the evolution could be divided into four possible phases approximately: exponential decay, no decay, power-law decay and exponential decay again. The model of magnetic fields expulsion induced by spin-down suggests that the magnetic fields decay only in a period between 10⁷yr and 10⁸yr.