There are two active and independent lines of research that aim at quantifying the amount of information that is revealed by computing on confidential data. Each line of research has developed its own notion of confidentiality: on the one hand, differential privacy is the emerging consensus guarantee used for privacy-preserving data analysis. On the other hand, information-theoretic notions of leakage are used for characterizing the confidentiality properties of programs in language-based settings. In this talk I will present recent work where we establish the first formal connections between both notions of confidentiality, and where we compare them in terms of the security guarantees they deliver. Joint work with Gilles Barthe.