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Functional programming, and in particular functional iteration, is one of those idiomatic aspects of Mathematica that takes some time to master. The benefits of functional iteration include increased efficiency and elegance, and a greatly-lowered propensity for certain types of errors. The rich variety of the available commands means that it's possible to find a functional solution to nearly any iteration problem; however, this same variety often discourages casual users from attempting to learn how to use those commands. In this article, we attempt to impose some order on the menagerie of Mathematica commands for iterating functionally. The commands are presented in the order of the prosaic to the esoteric, and practical examples are given for each one.
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