Privacy-preserving statistical data analysis addresses the general question of protecting privacy when publicly releasing information about a sensitive dataset. A privacy attack takes seemingly innocuous released information and uses it to discern the private details of individuals, thus demonstrating that such information compromises privacy. For example, re-identification attacks have shown that it is easy to link supposedly de-identified records to the identity of the individual concerned. This survey focuses on attacking aggregate data, such as statistics about how many individuals have a certain disease, genetic trait, or combination thereof. We consider two types of attacks: reconstruction attacks, which approximately determine a sensitive feature of all the individuals covered by the dataset, and tracing attacks, which determine whether or not a target individual's data are included in the dataset.Wealso discuss techniques from the differential privacy literature for releasing approximate aggregate statistics while provably thwarting any privacy attack.