As vision-language models (VLMs) are increasingly used in various applications, their trustworthiness becomes critical. This paper explores key dimensions of VLM trustworthiness-accuracy, fairness, safety, and robustness. We review methods to enhance visual-textual alignment and tackle challenges like adversarial attacks, biases, and privacy risks through innovative vulnerability assessment frameworks. Our findings highlight ongoing trustworthiness challenges despite some progress. We propose a research agenda emphasizing interdisciplinary approaches to address these gaps and promote responsible VLM deployment.