Theory of Mind is an essential ability of humans to infer the mental states of others. Here we provide a coherent summary of the potential, current progress, and problems of deep learning approaches to Theory of Mind. We highlight that many current findings can be explained through shortcuts. These shortcuts arise because the tasks used to investigate Theory of Mind in deep learning systems have been too narrow. Thus, we encourage researchers to investigate Theory of Mind in complex open-ended environments. Furthermore, to inspire future deep learning systems we provide a concise overview of prior work done in humans. We further argue that when studying Theory of Mind with deep learning, the research's main focus and contribution ought to be opening up the network's representations. We recommend researchers use tools from the field of interpretability of AI to study the relationship between different network components and aspects of Theory of Mind.