The advancements in deep learning-based methods for visual perception tasks have seen astounding growth in the last decade, with widespread adoption in a plethora of application areas from autonomous driving to clinical decision support systems. Despite their impressive performance, these deep learning-based models remain fairly opaque in their decision-making process, making their deployment in human-critical tasks a risky endeavor. This in turn makes understanding the decisions made by these models crucial for their reliable deployment. Explainable AI (XAI) methods attempt to address this by offering explanations for such black-box deep learning methods. In this paper, we provide a comprehensive survey of attribution-based XAI methods in computer vision and review the existing literature for gradient-based, perturbation-based, and contrastive methods for XAI, and provide insights on the key challenges in developing and evaluating robust XAI methods.