We are entering an era of ubiquitous genetic information for research, clinical care and personal curiosity. Sharing these data sets is vital for progress in biomedical research. However, a growing concern is the ability to protect the genetic privacy of the data originators. Here, we present an overview of genetic privacy breaching strategies. We outline the principles of each technique, indicate the underlying assumptions, and assess their technological complexity and maturation. We then review potential mitigation methods for privacy-preserving dissemination of sensitive data and highlight different cases that are relevant to genetic applications.