  This is mainly a survey article on the recent development of the theory of
graph-like Legendrian unfoldings and its applications. The notion of big
Legendrian submanifolds was introduced by Zakalyukin for describing the wave
front propagations. Graph-like Legendrian unfoldings belong to a special class
of big Legendrian submanifolds. Although this is a survey article, some new
original results and the corrected proofs of some results are given.
