A brief description is given of the basic concepts which arise in percolation theory. The nature of the percolation transition is illustrated by ‘snapshot’ frames from a film of a Monte Carlo simulation of a percolation process with the percolation probability varying from 0 to 1.21 pc, (where pc, is the critical probability). The largest cluster is identified in each frame, and when p is near to pc, this cluster approaches the boundaries. Finally, a short description is given of some more sophisticated percolation problems. © 1980 Taylor & Francis Group, LLC.