Shredders used to use a simple method – they cut the paper into very thin lines, that were totally unreadable.
Or, at least, so everybody thought. After the takeover of the American embassy in Teheran (something like 1972?), Iran’s new security forces just gave enough people enough time, and results were achieved. Many CIA and state-department documents were recombined, often causing embarrassment as Iranians told different countries in the world what the US really thought about them.
Since that day, shredders cut the paper into really tiny small square thingies.