Large language models (LLMs) have significant potential for intelligent tutoring systems (ITS), particularly in knowledge tracing (KT). Many current studies exhibit diverse approaches to LLM-based KT. However, despite the growing body of research, there is a lack of a consistent taxonomy for integrating LLMs into KT. In response, this study proposes a systematic taxonomy that categorizes the various roles LLMs can play in KT into three categories: LLM-enhanced, LLM-integrated, and LLM-standalone. Using this taxonomy, we systematically review and analyze studies published over the past three years that incorporate LLMs into knowledge tracing. Our analysis reveals that the role of LLMs, their strengths and weaknesses, and the type of data used, metrics vary across these categories. We also discuss the major challenges faced by each taxonomy, including optimizing feature fusion, handling real-time and unstructured inputs, designing effective prompts, and ensuring explainability. This comprehensive review provides a conceptual foundation and directions for future research in ITS driven by generative AI.