Fossil magnetic fields (i.e. fields that survive from one stage ofstellar evolution to a significantly later epoch withoutbeing regenerated) have been invoked to explain phenomena in the Sun, magnetic CP stars, white dwarfsand neutron stars. The feasibility of such processes is discussed critically. Estimates are made that suggest that flux survivalthrough pre-main sequence evolution is more likely to occur in stars withM > 1 M⊙. Any link between CP star and white dwarf magnetism is argued to favour the fossil field origin of CP star fields.