All-solid-state local oscillators in the terahertz frequency range are especially needed for space-borne radio astronomy and remote sensing of the atmosphere. Because solid-state oscillators cannot yet produce the necessary local oscillator power at submillimeter wavelengths, frequency multipliers are needed. So far, submillimeter-wave frequency multipliers are mainly based on a whisker-contacted Schottky diode as the nonlinear element. This paper discusses the multiplier theory and tools for analysis and design of millimeter- and submillimeter-wave multipliers. Experimental work is reviewed The Schottky diode model at submillimeter frequencies, use of Schottky multiplier chains versus direct higher-order multipliers, and the effect of cooling on Schottky diode multipliers are discussed. Alternative diodes such as the high electron mobility varactor (HEMV), the barrier-intrinsic-n+ diode (BIN), the barrier-n-n+ diode (BNN), the quantum well diode (QWD), and the single barrier varactor (SBV) are discussed, with attention also given to their potential as submillimeter frequency multipliers.