Differential privacy has emerged as a powerful tool to reason rigorously about privacy and confidentiality issues. In its purest form, differential privacy limits direct access to raw data, allowing interaction only through a noisy interface. This requires new approaches to statistical inference. In this talk, I will introduce the definition of differential privacy, followed by some of its key properties. I will present a framework for performing statistical inference under the constraint of differential privacy and its connections to measurement error and missing data models. The primary focus will be on constructing honest differentially private confidence intervals. I will present nearly optimal differentially private confidence intervals along with matching lower bounds, up to logarithmic factors. These intervals serve as important building blocks for more complex inference and data analysis problems. If time permits, I will also briefly describe my work on differential privacy in networks and adaptive data analysis. I will end with a demonstration of a differentially private interface to access data, developed as a part of ongoing collaboration between computer scientists, political scientists, and lawyers at Harvard.