Deep learning models are bad at signalling failure: They can make predictions with high confidence, and this is problematic in real-world applications such as healthcare, self-driving cars, and natural language systems, where there are considerable safety implications, or where there are discrepancies between the training data and data that the model makes predictions on. There is a pressing need both for understanding when models should not make predictions and improving model robustness to natural changes in the data. We'll give an overview of this problem setting. We also highlight promising avenues from recent work, including methods which average over multiple neural network predictions such as Bayesian neural nets and ensembles; as well as the recent surge in large pretrained models.