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.

44 pages, 20 figures, a review article to be published in Reports on Progress in Physics