Mental health is increasingly critical in contemporary healthcare, with psychotherapy demanding dynamic, context-sensitive interactions that traditional NLP methods struggle to capture. Large Language Models (LLMs) offer significant potential for addressing this gap due to their ability to handle extensive context and multi-turn reasoning. This review introduces a conceptual taxonomy dividing psychotherapy into interconnected stages--assessment, diagnosis, and treatment--to systematically examine LLM advancements and challenges. Our comprehensive analysis reveals imbalances in current research, such as a focus on common disorders, linguistic biases, fragmented methods, and limited theoretical integration. We identify critical challenges including capturing dynamic symptom fluctuations, overcoming linguistic and cultural biases, and ensuring diagnostic reliability. Highlighting future directions, we advocate for continuous multi-stage modeling, real-time adaptive systems grounded in psychological theory, and diversified research covering broader mental disorders and therapeutic approaches, aiming toward more holistic and clinically integrated psychotherapy LLMs systems.