AbstractThe minimization of the functionals defined by the prior knowledge and integral data of a neutron spectrum can be the basis of many unfolding methods. The form of these functionals classifies the widely used methods: FERDOR, SPECTRA, RFSP, CRYSTAL BALL, SAND-II, STAYSL, and others. The methods are systematically derived and theoretically compared to each other. Their relations to the function expansion method are discussed, and several cases of estimated spectra are studied. Treatments of response-function errors are also mentioned.