Randomized response (RR) was introduced as a technique for protecting respondent's privacy in survey interviews regarding sensitive characteristics. In recent years, the basic RR ideas have been used and extended in other contexts. We discuss usage and recent advances of RR in condentiality protection and in privacy preserving data mining. Wediscuss important differences between RR surveys and RR for condentiality protection. Inparticular, for condentiality protection, the data may be used to choose randomization probabilities suitably, but by doing so also makes well known inferences derived for RR surveys inapplicable. We examine one privacy breach criterion in data mining and proposea new privacy guarantee and a method for achieving that. We also discuss several newchallenges and open problems for future research.