  Explosive Percolation describes the abrupt onset of large-scale connectivity
that results from a simple random process designed to delay the onset of the
transition on an underlying random network or lattice. Explosive percolation
transitions exhibit an array of novel universality classes and supercritical
behaviors including a stochastic sequence of discontinuous transitions,
multiple giant components, and lack of self-averaging. Many mechanisms that
give rise to explosive percolation have been discovered, including overtaking,
correlated percolation, and evolution on hierarchical lattices. Many
connections to real-world systems, ranging from social networks to nanotubes,
have been identified and explosive percolation is an emerging paradigm for
modeling these systems as well as the consequences of small interventions
intended to delay phase transitions. This review aims to synthesize existing
results on explosive percolation and to identify fruitful directions for future
research.
