  Recent rapid progress in time domain surveys makes it possible to detect
various types of explosive transients in the Universe in large numbers, some of
which will be gravitationally lensed into multiple images. Although a large
number of strongly lensed distant galaxies and quasars have already been
discovered, strong lensing of explosive transients opens up new applications,
including improved measurements of cosmological parameters, powerful probes of
small scale structure of the Universe, and new observational tests of dark
matter scenarios, thanks to their rapidly evolving light curves as well as
their compact sizes. In particular, compact sizes of emitting regions of these
transient events indicate that wave optics effects play an important role in
some cases, which can lead to totally new applications of these lensing events.
Recently we have witnessed first discoveries of strongly lensed supernovae, and
strong lensing events of other types of explosive transients such as gamma-ray
bursts, fast radio bursts, and gravitational waves from compact binary mergers
are expected to be observed soon. In this review article, we summarize the
current state of research on strong gravitational lensing of explosive
transients and discuss future prospects.
