While deep learning has demonstrable success on many tasks, the point estimates provided by standard deep models can lead to overfitting and provide no uncertainty quantification on predictions. However, when models are applied to critical domains such as autonomous driving, precision health care, or criminal justice, reliable measurements of a model’s predictive uncertainty may be as crucial as correctness of its predictions. In this talk, we examine a number of deep (Bayesian) models that promise to capture complex forms for predictive uncertainties, we also examine metrics commonly used to such uncertainties. We aim to highlight strengths and limitations of these models as well as the metrics; we also discuss ideas to improve both in meaningful ways for downstream tasks.