Although chatbots have existed for decades, the emergence of transformer-based large language models (LLMs) has captivated the world through the most recent wave of artificial intelligence chatbots, including ChatGPT. Transformers are a type of neural network architecture that enables better contextual understanding of language and efficient training on massive amounts of unlabeled data, such as unstructured text from the internet. As LLMs have increased in size, their improved performance and emergent abilities have revolutionized natural language processing. Since language is integral to human thought, applications based on LLMs have transformative potential in many industries. In fact, LLM-based chatbots have demonstrated human-level performance on many professional benchmarks, including in radiology. LLMs offer numerous clinical and research applications in radiology, several of which have been explored in the literature with encouraging results. Multimodal LLMs can simultaneously interpret text and images to generate reports, closely mimicking current diagnostic pathways in radiology. Thus, from requisition to report, LLMs have the opportunity to positively impact nearly every step of the radiology journey. Yet, these impressive models are not without limitations. This article reviews the limitations of LLMs and mitigation strategies, as well as potential uses of LLMs, including multimodal models. Also reviewed are existing LLM-based applications that can enhance efficiency in supervised settings.