The Fast Radio Burst (FRBs) are millisecond duration dispersed radio transients signals which have now been observed at various single-dish radio telescopes, but for which no counterpart was identified so far at other electromagnetic bands. Models of the host galaxy and of the intergalactic medium suggest that they may have cosmological redshifts in the 0.5 to 1 range and distances of up to 3 Gpc. However, other models have proposed a galactic origin. The talk will report on the current status of the research about these radio sources, and will introduce the SUPERB survey at Parkes, which is the best experiment now running for discovering additional events of this class.