Gamma-Ray, Neutron, and Alpha-Particle Spectrometers (GRS, NS, and APS, respectively) were included in the payload complement of Lunar Prospector (LP). Specific objectives of the GRS were to map abundances of Fe, Ti, Th, K, Si, O, Mg, Al, and Ca to depths of 20 cm. Those of the NS were to search for water ice to depths of 100 cm near the lunar poles and to map regolith maturity. Objectives of the APS were to search for, map, and provide a measure of the time history of gaseous release events at the lunar surface. The purpose of this paper is to document the mechanical, analog electronic, digital electronic, and microprocessor designs of the suite of spectrometers, present a representative sample of the calibrated response functions of all sensors, and document the operation of all three LP spectrometers in sufficient detail as to enable the full knowledgeable use of all data products that were archived in the Planetary Data System for future use by the planetary-science community.