In recent years, significant advancements in the field of machine learning have influenced the domain of image restoration. While these technological advancements present prospects for improving the quality of images, they also present difficulties, particularly the proliferation of manipulated or counterfeit multimedia information on the internet. The objective of this paper is to provide a comprehensive review of existing inpainting algorithms and forgery detections, with a specific emphasis on techniques that are designed for the purpose of removing objects from digital images. In this study, we will examine various techniques encompassing conventional texture synthesis methods, as well as those based on neural networks. Furthermore, we will explore the artifacts associated with the identification of modified photos and present the artifacts frequently introduced by the inpainting procedure and assess the state-of-the-art technology for detecting such modifications. Lastly, we shall look at the available datasets and how the methods compare with each other. Having covered all of the above, the final outcome of this study is to provide a comprehensive perspective on the abilities and constraints to detect images for which an inpainting object removal method was applied.