The development of next-step neutron spectrometers for use on high-power (especially burning) fusion plasmas is described. The expected performance specifications of optimized designs are compared with the fundamental limits of neutron diagnostics set by the underlying nuclear reactions for neutron detection. The potential results of the next-step spectrometers on the International Thermonuclear Experimental Reactor (ITER) and the Joint European Torus (JET) are illustrated, especially those derivable from details in the single-component neutron spectrum of thermal ion reactions and from the separation of thermal and suprathermal ion reactions in multiple-component spectra. The information content and its relationship to the quality of neutron spectrometry data are illustrated, and some implications on alpha-particle issues are discussed.