Thomas Steinke IBM Almaden Research Center Private data analysis is not a one-off event. Sensitive data will be collected and used repeatedly by different entities throughout an individual's lifetime. Thus it vital to understand how privacy risks accumulate over multiple independent analyses. One of the hallmarks of differential privacy is that we can prove quantitative bounds on how privacy degrades under this composition process. In this talk I will discuss recent work on concentrated differential privacy that seeks to prove the tightest possible bounds on how privacy composes.