  Fast radio bursts (FRBs), millisecond-duration bursts prevailing in the radio
sky, are the latest big puzzle in the universe and have been a subject of
intense observational and theoretical investigations in recent years. The rapid
accumulation of the observational data has painted the following sketch about
the physical origin of FRBs: They predominantly originate from cosmological
distances so that their sources produce the most extreme coherent radio
emission in the universe; at least some, probably most, FRBs are repeating
sources that do not invoke cataclysmic events; and at least some FRBs are
produced by magnetars, neutron stars with the strongest magnetic fields in the
universe. Many open questions regarding the physical origin(s) and mechanism(s)
of FRBs remain. This article reviews the phenomenology and possible underlying
physics of FRBs. Topics include: a summary of the observational data, basic
plasma physics, general constraints on FRB models from the data, radiation
mechanisms, source and environment models, propagation effects, as well as FRBs
as cosmological probes. Current pressing problems and future prospects are also
discussed.
