  During the past two decades, percolation has long served as a basic paradigm
for network resilience, community formation and so on in complex systems. While
the percolation transition is known as one of the most robust continuous
transitions, the percolation transitions occurring in complex systems are often
of different types such as discontinuous, hybrid, and infinite-order phase
transitions. Thus, percolation has received considerable attention in network
science community. Here we present a very brief review of percolation theory
recently developed, which includes those types of phase transitions, critical
phenomena, and finite-size scaling theory. Moreover, we discuss potential
applications of theoretical results and several open questions including
universal behaviors.
