Percolation in anisotropic, hyperbolic and small-world lattices and in explosive growth

Percolation on a large variety of systems is discussed. A variety of lattices where exact and approximate solutions of the criticality condition, including anisotropic systems, are considered. Also, hyperbolic systems, such as the heptagonal lattice, are studied with respect to a crossing criterion for percolation to hold. Hierarchical small-world ``Hanoi" lattices and randomized versions are considered as well. Finally, the effects of biased cluster growth by the ``Achlioptas" process, and the resulting explosive cluster growth, are considered. The overall picture shows the richness and complexity of percolation processes, and the existence of many open problems.