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. This paper outlines recent methods in deep learning for constructing such models from data and learning to use them via reinforcement learning, and compares such approaches to human mental simulation. Model-based methods in deep learning can serve as powerful tools for building and scaling cognitive models. However, a number of challenges remain in matching the capacity of human mental simulation for efficiency, compositionality, generalization, and creativity.