Differential privacy is a parameterized notion of database privacy that gives a mathematically rigorous worst-case bound on the maximum amount of information that can be learned about an individual's data from the output of a computation. Recent work has provided tools for differentially private stochastic gradient decent, which enables differentially private deep learning. These in turn enable differentially private synthetic data generation, to provide synthetic versions of sensitive datasets that share statistical properties with the original data while additionally providing formal privacy guarantees for the training dataset. This talk will first give an introduction to differential privacy, and then survey recent advances in differentially private deep learning and its application to synthetic data generation.