Image inpainting is currently a hot topic within the field of computer vision. It offers a viable solution for various applications, including photographic restoration, video editing, and medical imaging. Deep learning advancements, notably convolutional neural networks (CNNs) and generative adversarial networks (GANs), have significantly enhanced the inpainting task with an improved capability to fill missing or damaged regions in an image or video through the incorporation of contextually appropriate details. These advancements have improved other aspects, including efficiency, information preservation, and achieving both realistic textures and structures. Recently, visual transformers have been exploited and offer some improvements to image or video inpainting. The advent of transformer-based architectures, which were initially designed for natural language processing, has also been integrated into computer vision tasks. These methods utilize self-attention mechanisms that excel in capturing long-range dependencies within data; therefore, they are particularly effective for tasks requiring a comprehensive understanding of the global context of an image or video. In this paper, we provide a comprehensive review of the current image or video inpainting approaches, with a specific focus on transformer-based techniques, with the goal to highlight the significant improvements and provide a guideline for new researchers in the field of image or video inpainting using visual transformers. We categorized the transformer-based techniques by their architectural configurations, types of damage, and performance metrics. Furthermore, we present an organized synthesis of the current challenges, and suggest directions for future research in the field of image or video inpainting.