  The past decades have witnessed a lot of progress in gravitational lensing
with two main targets: stars and galaxies (with active galactic nuclei). The
success is partially attributed to the continuous luminescence of these sources
making the detection and monitoring relatively easy. With the running of
ongoing and upcoming large facilities/surveys in various electromagnetic and
gravitational-wave bands, the era of time-domain surveys would guarantee
constant detection of strongly lensed explosive transient events, for example,
supernovae in all types, gamma ray bursts with afterglows in all bands, fast
radio bursts and even gravitational waves. Lensed transients have many
advantages over the traditional targets in studying the Universe and
magnification effect helps to understand the transients themselves at high
redshifts. In this review article, basing on the recent achievements in the
literature, we summarize the methods of searching for different kinds of lensed
transient signals, the latest results on detection and their applications in
fundamental physics, astrophysics and cosmology. At the same time, we give
supplementary comments as well as prospects of this emerging research direction
that may help readers who are interested in entering this field.
