Universal scaling functions and quantities in percolation models

We briefly review recent work on universal finite-size scaling functions (UFSSFs) and quantities in percolation models. The topics under discussion include: (a) UFSSFs for the existence probability (also called crossing probability) Ep, the percolation probability P, and the probability Wn of the appearance of n percolating clusters, (b) universal slope for average number of percolating clusters, (c) UFSSFs for a q-state bond-correlated percolation model corresponding to the q-state Potts model. We also briefly mention some very recent related developments and discuss implications of our results.