Universal scaling functions and quantities in percolation models

We briefly review recent work on universal finite-size scaling functions (U FSSFs) and quantities in percolation models. The topics under discussion in clude: (a) UFSSFs for the existence probability (also called crossing proba bility) E-p, the percolation probability P, and the probability W-n of the appearance of n percolating clusters, (b) universal slope for average numbe r of percolating clusters, (c) UFSSFs for a q-state bond-correlated percola tion model corresponding to the q-state Potts model. We also briefly mentio n some very recent related developments and discuss implications of our res ults. (C) 1999 Elsevier Science B.V. All rights reserved.