Face recognition has gone from scientific novelty to one of the most pervasive biometric modalities used by people around the world. Today, face recognition systems power everything from our smartphone lock screens to border checkpoints at airports, analysis of shopper demographics in retail stores, and citywide security camera networks. In this survey, we chronicle recent advances in automatic face recognition technology, covering research from approximately the past 20 years. We divide the related literature into three main periods: work in the classical era up until 20 10 focused on techniques such as statistical models and texture descriptors, research from 2010 - 2020 centered around deep convolutional models and margin-based losses, and finally methods from the past few years based on transformers and diffusion models as well as a re-focus on fairness and efficiency. Within each of these broad categories, we highlight key ideas behind each family of algorithms including how their objective function helps them learn a useful representation and what tradeoffs that might introduce. We also aggregate many of the reported benchmarks, dataset information, and loss functions in tables for convenient comparison. Finally, we discuss areas of concern that still remain such as biases, adversarial examples, and data privacy laws, and highlight promising directions for future work including self-supervised learning, interpretability, and data generation.