This systematic literature review examines the role of large language models (LLMs) in UI/UX design, synthesizing findings from 38 peer-reviewed studies published between 2022 and 2025. We identify key LLMs in use, including GPT-4, Gemini, and PaLM, and map their integration across the design lifecycle, from ideation to evaluation. Common practices include prompt engineering, human-in-the-loop workflows, and multimodal input. While LLMs are reshaping design processes, challenges such as hallucination, prompt instability, and limited explainability persist. Our findings highlight LLMs as emerging collaborators in design, and we propose directions for the ethical, inclusive, and effective integration of these technologies.