  The discovery of radio pulsars over a half century ago was a seminal moment
in astronomy. It demonstrated the existence of neutron stars, gave a powerful
observational tool to study them, and has allowed us to probe strong gravity,
dense matter, and the interstellar medium. More recently, pulsar surveys have
led to the serendipitous discovery of fast radio bursts (FRBs). While FRBs
appear similar to the individual pulses from pulsars, their large dispersive
delays suggest that they originate from far outside the Milky Way and hence are
many orders-of-magnitude more luminous. While most FRBs appear to be one-off,
perhaps cataclysmic events, two sources are now known to repeat and thus
clearly have a longer-lived central engine. Beyond understanding how they are
created, there is also the prospect of using FRBs -- as with pulsars -- to
probe the extremes of the Universe as well as the otherwise invisible
intervening medium. Such studies will be aided by the high implied all-sky
event rate: there is a detectable FRB roughly once every minute occurring
somewhere on the sky. The fact that less than a hundred FRB sources have been
discovered in the last decade is largely due to the small fields-of-view of
current radio telescopes. A new generation of wide-field instruments is now
coming online, however, and these will be capable of detecting multiple FRBs
per day. We are thus on the brink of further breakthroughs in the
short-duration radio transient phase space, which will be critical for
differentiating between the many proposed theories for the origin of FRBs. In
this review, we give an observational and theoretical introduction at a level
that is accessible to astronomers entering the field.
