Large Language Models (LLMs) are reshaping recommender systems by enabling more semantic, generative, and interactive recommendation pipelines. However, this shift also introduces new fairness challenges, as biases may arise from pretrained knowledge, prompts, generated explanations, decoding strategies, and feedback loops. This survey provides a systematic review of fairness in LLM based recommender systems, organizing existing studies through a two-dimensional view of bias mechanisms and fairness targets, together with a structured overview of the evaluation landscape and mitigation strategies. We further connect fairness with broader trustworthy concerns, including explainability, privacy, robustness, and controllability. To the best of our knowledge, this is the first survey specifically focused on fairness in LLM-based recommender systems, aiming to provide a structured foundation for future research on comprehensive and reliable fairness evaluation in LLM-based recommender systems.