Abstract: I will describe several applications of machine learning to accelerate numerical studies of field theories, which are important in contexts from statistical mechanics and condensed matter physics to nuclear and particle physics. In particular, lattice field theory calculations require the evaluation of integrals over field configurations; typically this is done via importance sampling, with correctly-distributed samples of field configurations generated via a Markov chain Monte Carlo approach (MCMC). I will outline different approaches to this task based on machine learning, including using neural networks for the matching of field configurations at different scales in multi-scale approaches to MCMC, and alternatively using normalising flows for the direct sampling of field configurations. I will also outline the challenges in these applications, which include in particular scaling the algorithms to the systems of 10^12 variables which correspond to state-of-the-art calculations.