For the last several years, Google has been leading the development and real-world deployment of state-of-the-art, practical techniques for learning statistics and ML models with strong privacy guarantees for the data involved.  I'll give an overview of our work, and the practical techniques we've developed for training Deep Neural Networks with strong  privacy guarantees.  In particular, I'll cover recent results that show how local differential privacy guarantees can be strengthened by the addition of anonymity, and explain the motivation for that work. I'll also cover recent work on uncovering and measuring privacy problems due to unintended memorization in machine learning models.