Reduction of the carrier level permits higher power levels in the sidebands than would be possible with conventional AM transmission. Carrier power must be restored by the receiving station to permit demodulation, usually by means of a beat frequency oscillator (BFO). Failure of the BFO to match the original carrier frequency when receiving such a signal will cause a heterodyne.
Suppressed carriers are often used for single sideband (SSB) transmissions, such as for amateur radio on shortwave. That system is referred to in full as SSB suppressed carrier (SSBSC) or (SSB-SC). International broadcasters agreed in 1985 to also use SSBSC entirely by 2015, though IBOC and IBAC digital radio (namely Digital Radio Mondiale) seems likely to make this irrelevant.
FM stereo transmissions use a double-sideband suppressed carrier (DSBSC) signal from a stereo generator, together with a pilot tone of exactly half the original carrier frequency. This allows reconstitution of the original stereo carrier, and hence the stereo signal.
Source: partly from Federal Standard 1037C
See also Carrier recovery.