The randomized response survey model introduced in 1965 by Warner is reviewed and applied to the analysis of contaminated data, that is, response or reported data that is truthful with probability less than one. Two generic mechanisms are distinguished: an active mechanism whereby the contamination is inserted into the process and hence becomes a statistical design parameter, and a passive mechanism whereby contamination of the response is suspected and hence becomes an analysis parameter. The impact of contamination on the operating characteristics of some common statistical inference procedures is developed for binomial models.