Neutron-induced fission cross sections have been deduced from measured fission probabilities for targets of Tb-231,Tb-233, U-234,U-235,U-235m,U-236,U-237,U-239, Np-236,Np-236m,Np-237,Np-238, Pu-237,Pu-237m,Pu-240,Pu-241,Pu-243, and (240,241,242,242m,243,244,244m)AM. The fission-probability data were measured for (t, pf) reactions, up to an equivalent incident neutron energy of E-n similar to 2.2 MeV, and for (He-3,xf) reactions, up to an equivalent E-n similar to 6 MeV. The procedure used to deduce cross sections for the corresponding (n,f) reactions, within the equivalent neutron-energy range of the fission-probability data, is briefly reviewed. The deduced (n,f) cross sections obtained to date are summarized. The limitations of the present formalism and proposed improvements are discussed, within the context of extending the (n,f) cross sections beyond the range of the fission-probability data, up to E-n = 20 MeV.