Large-scale deep neural networks have emerged as a powerful approach to predictive tasks in a broad range of domains. However, they are apt to fail in subtle and unexpected ways when applied to tasks beyond their training data. In this talk, I will show how probabilistic inference can be used to improve the design and validation of neural networks. First, I will discuss how meta-learning can be used to endow neural networks with favorable inductive biases from probabilistic models. Second, I will illustrate how to flexibly quantify the performance of black-box predictive algorithms by using tools from empirical process theory. I will conclude with directions for future work aimed at building deep learning algorithms that are robust to changing circumstances and are able to produce reliable estimates of uncertainty.