State-of-the-art AI models largely lack an understanding of the cause-effect relationship that governs human understanding of the real world. Consequently, these models do not generalize to unseen data, often produce unfair results, and are difficult to interpret. This has led to efforts to improve the trustworthiness aspects of AI models. Recently, causal modeling and inference methods have emerged as powerful tools. This review aims to provide the reader with an overview of causal methods that have been developed to improve the trustworthiness of AI models. We hope that our contribution will motivate future research on causality-based solutions for trustworthy AI.