The hybrid B3PW91 exchange-correlation functional is used to calculate hyperfine fields at lanthanide and actinide impurities in Fe. We show this functional to provide results similar to the ones obtained by LDA+U for lanthanides, while it turns out to be superior to LDA+U for actinides. The amount of Hartree-Fock exchange that is needed in B3PW91 is considerably larger than the 20% typically needed for molecules. Lanthanides couple ferrimagnetically to Fe and are mostly trivalent, except for the divalent Yb. The same would be true for the actinides, provided localization in the actinide series sets in before Cf. The experimental and theoretical evidence for this is discussed. Trends in the orbital, dipolar, and Fermi contact hyperfine fields and in the electric-field gradient are explained. The effect of the relativistic mass enhancement on the dipolar hyperfine field is examined. Experiments that can answer some of the remaining key questions are suggested.