Particle physics aims to answer profound questions about the fundamental building blocks of the Universe through enormous data sets collected at experiments like the Large Hadron Collider at CERN. Inference in this context involves two extremes. On one hand the theories of fundamental particle interactions are described by quantum field theory, which is elegant, highly constrained, and highly predictive. On the other hand, the observations come from interactions with complex sensor arrays with uncertain response, which lead to intractable likelihoods. Machine learning techniques with high-capacity models offer a promising set of tools for coping with the complexity of the data; however, we ultimately want to perform inference in the language of quantum field theory. I will discuss likelihood-free inference, generative models, adversarial training, and other recent progress in machine learning from this point of view.