Data collected by organizations and agencies are a key resource in today's information age. The use of sophisticated data mining techniques makes it possible to extract relevant knowledge that can then be used for a variety of purposes, such as research, developing innovative technologies and services, intelligence and counter-terrorism operations, and providing inputs to public policy making. However the disclosure of those data poses serious threats to individual privacy. In this talk, we present a novel privacy framework that we call Membership Privacy, which prevents the adversary from significantly increasing its ability to conclude that an entity is in the input dataset. Membership privacy is parameterized by a family of distributions that captures the adversary's prior knowledge. The power and flexibility of the proposed framework lies in the ability to choose different distribution families to instantiate membership privacy. Many privacy notions in the literature are equivalent to membership privacy with interesting distribution families, including differential privacy, differential identifiability, and differential privacy under sampling. The framework also provides a principled approach to developing new privacy notions under which better utility can be achieved than what is possible under differential privacy. This is joint work with Wahbeh Qardaji, Dong Su, Yi Wu, and Weining Yang.