At the heart of radiological practice is the challenge of integrating complex imaging data with clinical information to produce actionable insights. Nuanced application of language is key for various activities, including managing requests, describing and interpreting imaging findings in the context of clinical data, and concisely documenting and communicating the outcomes. The emergence of large language models (LLMs) offers an opportunity to improve the management and interpretation of the vast data in radiology. Despite being primarily general-purpose, these advanced computational models demonstrate impressive capabilities in specialized language-related tasks, even without specific training. Unlocking the potential of LLMs for radiology requires basic understanding of their foundations and a strategic approach to navigate their idiosyncrasies. This review, drawing from practical radiology and machine learning expertise and recent literature, provides readers insight into the potential of LLMs in radiology. It examines best practices that have so far stood the test of time in the rapidly evolving landscape of LLMs. This includes practical advice for optimizing LLM characteristics for radiology practices along with limitations, effective prompting, and fine-tuning strategies.