The growth of two-dimensional (2D) materials through chemical vapor deposition (CVD) has sparked a growing interest among both the industrial and academic communities. The interest stems from several key advantages associated with CVD, including high yield, high quality, and high tunability. In order to harness the application potentials of 2D materials, it is often necessary to transfer them from their growth substrates to their desired target substrates. However, conventional transfer methods introduce contamination that can adversely affect the quality and properties of the transferred 2D materials, thus limiting their overall application performance. This review presents a comprehensive summary of the current clean transfer methods for 2D materials with a specific focus on the understanding of interaction between supporting layers and 2D materials. The review encompasses various aspects, including clean transfer methods, post-transfer cleaning techniques, and cleanliness assessment. Furthermore, it analyzes and compares the advances and limitations of these clean transfer techniques. Finally, the review highlights the primary challenges associated with current clean transfer methods and provides an outlook on future prospects.