While
While[test, body] evaluates test, then body, repetitively, until test first fails to give True.
While[test] does the loop with a null body.
If Break[ ] is generated in the evaluation of body, the While loop exits.
Continue[ ] exits the evaluation of body, and continues the loop.
Unless Return[ ] is generated, the final value returned by While is Null.
Example: i=0; While[i < 0, tot = tot + f[i]; i++]. Note that the roles of ; and , are reversed relative to the C programming language.
See The Mathematica Book on the web: Section 2.5.9.
See also: Do, For, NestWhile, Nest, Fold, Select.
Further Examples
