  Percolation has long served as a model for diverse phenomena and systems. The
percolation transition, that is, the formation of a giant cluster on a
macroscopic scale, is known as one of the most robust continuous transitions.
Recently, however, many abrupt percolation transitions have been observed in
complex systems. To illustrate such phenomena, considerable effort has been
made to introduce models and construct theoretical frameworks for explosive,
discontinuous, and hybrid percolation transitions. Experimental results have
also been reported. In this review article, we describe such percolation
models, their critical behaviors and universal features, and real-world
phenomena.
