News and views in discontinuous phase transitions

Recent progress in the theory of discontinuous percolation allow us to better understand the the sudden emergence of large-scale connectedness both in networked systems and on the lattice. We analytically study mechanisms for the amplification of critical fluctuations at the phase transition point, non-self-averaging and power law fluctuations. A single event analysis allow to establish criteria for discontinuous percolation transitions, even on the high-dimensional lattice. Some applications such as salad bowl percolation, and inverse fragmentation are discussed.