With the extensive application of Graph Neural Networks (GNNs) across various domains, their trustworthiness has emerged as a focal point of research. Some existing studies have shown that the integration of large language models (LLMs) can improve the semantic understanding and generation capabilities of GNNs, which in turn improves the trustworthiness of GNNs from various aspects. Our review introduces a taxonomy that offers researchers a clear framework for comprehending the principles and applications of different methods and helps clarify the connections and differences among various approaches. Then we systematically survey representative approaches along the four categories of our taxonomy. Through our taxonomy, researchers can understand the applicable scenarios, potential advantages, and limitations of each approach for the the trusted integration of GNNs with LLMs. Finally, we present some promising directions of work and future trends for the integration of LLMs and GNNs to improve model trustworthiness.