Bayesian optimization is a powerful and flexible tool for AutoML. While BayesOpt was first deployed for AutoML simply as a black-box optimizer, recent approaches perform grey-box optimization: they leverage capabilities and problem structure specific to AutoML such as freezing and thawing training, early stopping, treating cross-validation error minimization as multi-task learning, and warm starting from previously tuned models. We provide an overview of this area and describe recent advances for optimizing sampling-based acquisition functions that make grey-box BayesOpt significantly more efficient.