  Fast radio bursts (FRBs) are millisecond-timescale bursts of coherent radio
emission that are luminous enough to be detectable at cosmological distances.
In this review I describe the discovery of FRBs, subsequent advances in our
understanding of them, and future prospects. Thousands of potentially
observable FRBs reach Earth every day; they probably originate from highly
magnetic and/or rapidly rotating neutron stars in the distant Universe. Some
FRBs repeat, with this sub-class often occurring in highly magnetic
environments. Two repeaters exhibit cyclic activity windows, consistent with an
orbital period. One nearby FRB was from a Galactic magnetar during an X-ray
outburst. The host galaxies of some FRBs have been located, providing
information about the host environments and the total baryonic content of the
Universe.
