Minireview: New results for old percolation

Percolation theory deals with the formation of clusters in disordered media. At the percolation threshold for the first time an infinite cluster appears. However, research of the last years showed that at this phase transition some old ideas were wrong: There can also be two or three clusters spanning from top to bottom, even in large two-dimensional lattices; and the probability of spanning is not given by simple real-space renormalization ideas