Mental simulation—the capacity to imagine what will or what could be—is a salient feature of human cognition, playing a key role in a wide range of cognitive abilities. In artificial intelligence, the last few years have seen the development of methods which are analogous to mental models and mental simulation. In this talk, I will discuss recent methods in deep learning for constructing such models from data and learning to use them via reinforcement learning, and compare such approaches to human mental simulation. While a number of challenges remain in matching the capacity of human mental simulation, I will highlight some recent progress on developing more compositional and efficient model-based algorithms through the use of graph neural networks and tree search.