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In the last decades, deep learning (DL) has emerged as a powerful and dominant technique for solving challenging problems in various fields. Likewise, in the field of digital image forensics, a large and growing body of literature investigates DL-based techniques for detecting and classifying tampered regions in images. This article aims to provides a comprehensive survey of state-of-the-art DL-based methods for image-forgery detection. Copy-move images and spliced images, two of the most popular types of forged images, were considered. Recently, owing to advances in DL, DL-based approaches have yielded much better results as compared to traditional non-DL-based ones. The surveyed techniques were proposed by developing or fusing various efficient DL methods, such as CNN, RCNN, or LSTM to adapt to detecting tampered traces.