Neutron stars have strong magnetic fields that appear to evolve in time. I will discuss the evidence for this and what I believe to be important physical ingredients in the description of this process. Neutron stars are born hot, at which point they are (briefly) well described as a self-gravitating ball of normal (non-superfluid), highly conducting, and stably stratified fluid, which allows only certain magnetic field configurations, the simplest of which are axially symmetric, involving linked poloidal (meridional) and toroidal (azimuthal) components. Starting from such an initial configuration, various processes act in the way of modifying the magnetic field over long time scales. On the one hand, the crust freezes, stabilizing the magnetic field, although resistive diffusion, Hall drift or even breaking of the crust might overcome this. In the fluid core, ambipolar diffusion and beta decays can erode the stable stratification, destabilizing the magnetic field configuration, which is also likely to be affected by the progressive conversion of the protons into a superconducting state.

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