A review of the current state in the development of receivers with an extremely low noise level in the short-wave part of the millimeter (mm) and submillimeter (submm)-wave bands is presented. A superheterodyne with a mixer at the input remains the main type of such receivers. The mixers using superconductor-insulator-superconductor (SIS) tunnel contacts and having noise temperatures very close to the quantum limit dominate at frequencies of up to ~1 THz. At the higher frequencies, the best results were obtained with hot-electron bolometers as mixers where the strong dependence of the semiconductor resistance on the temperature Tc is employed. Examples of the SIS receivers and cooled Schottky-barrier diode (SBD) receivers developed at the Institute of Applied Physics of the Russian Academy of Sciences are slightly inferior to SIS receivers in noise temperature but are useful for many applications. The prospects of low-noise reception in the mm and submm-wave bands, in particular the prospects of using integrated receivers and multipath systems, are discussed. © 1999 Kluwer Academic / Plenum Publishers.