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We summarize our understanding of millisecond radio bursts from an extragalactic population of sources. Fast radio bursts (FRBs) occur at an extraordinary rate, thousands per day over the entire sky with radiation energy densities at the source about ten billion times larger than those from Galactic pulsars. We survey FRB phenomenology, source models and host galaxies, coherent radiation models, and the role of plasma propagation effects in burst detection. The FRB field is guaranteed to be exciting: New telescopes will expand the sample from the current ∼80 unique burst sources (and only a few secure localizations and redshifts) to thousands, with burst localizations that enable host-galaxy redshifts emerging directly from interferometric surveys.
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