We review the reasons that make superconductivity unlikely to arise in a ferromagnet. Then, in light of the report by Tallon and collaborators thatRuSr2GdCu2O8becomes superconducting at ∼35 K which is well below the Curie temperature of 132 K, we consider whether the objections really apply to this compound. Our considerations are supported by local spin density calculations for this compound, which indeed indicate a ferromagneticRuO2layer. The Ru moment resides int2gorbitals but is characteristic of itinerant magnetism (and is sensitive to choice of exchange-correlation potential and to the atomic positions). Based on the small exchange splitting that is induced in the Cu-O layers, the system seems capable of supporting singlet superconductivity an FFLO-type order parameter and possibly a &pgr;-phase alternation between layers. If instead the pairing is triplet in theRuO2layers, it can be distinguished by a spin-polarized supercurrent. Either type of superconductivity seems to imply a spontaneous vortex phase if the magnetization is rotated out of the plane. ©1999 American Institute of Physics.