  Recently, the authors showed that the critical probability for random Voronoi
percolation in the plane is 1/2. A by-product of the method was a short proof
of the Harris-Kesten Theorem concerning bond percolation in the planar square
lattice. The aim of this paper is to show that the same techniques can be
applied to many other planar percolation models, both to obtain short proofs of
known results, and to prove new ones.
