I tried three times to write something insightful about percolation theory, and decided I couldn't because I don't know enough about it. Yet. I'll be working on that. Meanwhile, I mention the topic at all because I'm seeing it appear in all sorts of contexts, from pore structures in low-k dielectrics to heterojunctions and carrier conduction mechanisms in advanced solar cells.
Percolation theory, as the name implies, looks at the way liquids infiltrate and work their way through porous media. Much of the early work was done by hydrologists, but the same mathematical formalism turns out to apply to many types of structure formation. In porous low-k dielectrics, for example, percolation affects conversion of the poragen, outgassing of any reaction byproducts, infiltration of moisture or other contaminants into the film, and so forth. Interesting stuff, and it's becoming more relevant as more electronic devices use materials that don't form nice uniform films.