This review explores the potential applications of Large Language Models (LLMs) in nuclear medicine, especially nuclear medicine examinations such as PET and SPECT, reviewing recent advancements in both fields. Despite the rapid adoption of LLMs in various medical specialties, their integration into nuclear medicine has not yet been sufficiently explored. We first discuss the latest developments in nuclear medicine, including new radiopharmaceuticals, imaging techniques, and clinical applications. We then analyze how LLMs are being utilized in radiology, particularly in report generation, image interpretation, and medical education. We highlight the potential of LLMs to enhance nuclear medicine practices, such as improving report structuring, assisting in diagnosis, and facilitating research. However, challenges remain, including the need for improved reliability, explainability, and bias reduction in LLMs. The review also addresses the ethical considerations and potential limitations of AI in healthcare. In conclusion, LLMs have significant potential to transform existing frameworks in nuclear medicine, making it a critical area for future research and development.