The field of recommender systems (RS) is currently undergoing two profound paradigm shifts. From the perspective of objectives, the goal has shifted beyond mere recommendation accuracy to comprehensive trustworthiness, encompassing multiple dimensions such as robustness, fairness, and privacy preservation. From a technical perspective, Large Language Models (LLMs) have been extensively integrated into RS, reshaping the foundations of recommendation through richer semantic understanding, stronger intent reasoning, and more flexible user interactions. The convergence of these two shifts prompts a timely and pivotal question: how does the integration of LLMs reshape the landscape of trustworthy recommendation? In this work, we present a systematic review of trustworthy LLM-empowered recommendation. By comprehensively analyzing over 200 recent studies, we reveal that the introduction of LLMs acts as a double-edged sword. While their advanced mechanisms and user-friendly interfaces offer unprecedented opportunities to enhance trustworthiness, they simultaneously introduce new risks, such as novel forms of bias and hallucination-induced issues. To characterize this dual impact, we systematically identify 13 opportunities and 18 challenges across six fundamental dimensions of trustworthiness, and accordingly organize the existing literature into a novel taxonomy. We also provide a comprehensive review of commonly used datasets and evaluation metrics to facilitate empirical validation. Finally, we identify critical open challenges and outline future directions, hoping to inspire future research on this emerging topic.