Fast radio bursts are mysterious millisecond-duration transients prevalent in the radio sky. Rapid accumulation of data in recent years has facilitated an understanding of the underlying physical mechanisms of these events. Knowledge gained from the neighboring fields of gamma-ray bursts and radio pulsars also offered insight. Here I review developments in this fast-moving field.Two generic categories of radiation model invoking either magnetospheres of compact objects (neutron stars or black holes) or relativistic shocks launched from such objects have been much debated. The recent detection of a Galactic fast radio burst in association with a soft gamma-ray repeater suggests that magnetar engines can produce at least some, and probably all, fast radio bursts. Other engines that could produce fast radio bursts are not required, but are also not impossible. On 24 July, 2001, a bright, dispersed radio pulse reached the Parkes 64-m telescope in Australia. The recorded signal remained unnoticed until Duncan Lorimer and his collaborators discovered it (now known as the fast radio burst FRB 010724) several years later and published the results in Science 1. For some time, some astronomers were not convinced that this so-called "Lorimer burst" was a genuine type of astrophysical event, until four more events were reported in 2013 (ref. 2). The field then enjoyed a rapid boost from both observational and theoretical fronts. With the identification of the microwave-oven-origin of some artificial bursts known as "perytons", the astrophysical origin of the bona fide bursts was finally established 3. This was followed by the detection of the first repeating source, known as FRB 121102 (ref. 4) and its localization in a dwarf star forming galaxy at redshift z = 0.19(refs. 5-7), establishing the extragalactic/cosmological origin (in contrast to the Galactic origin 8) of these events. Numerous theoretical models have been proposed to interpret these mysterious events 9. These have been driven by observations and groundbreaking results from numerous radio observatories: Parkes, Arecibo, Green Bank Telescope, the 1