Graphene is believed to have promising applications in many fields because of its unique properties. At present, graphene films are mainly prepared on Cu substrates by chemical vapor deposition. The graphene films prepared in this way need to be transferred to the target substrates for further applications, while the transfer process inevitably induces contamination on graphene, which affects the properties of graphene and the performance of devices. Therefore, how to reduce or avoid contamination and realize the clean transfer of graphene is an important topic for the development of graphene transfer technology, which is the major topic of this review. Here, firstly, the transfer techniques of graphene are briefly reviewed, which can be classified according to different rules. For example, it can be classified as direct transfer, with which graphene is directly stuck to the target substrate, and indirect transfer, with which graphene is indirectly transferred to the target substrate with a carrier film. According to the way of separating graphene and the growth substrate, it can also be classified as dissolving transfer, with which the substrate is dissolved by chemical etchant, and delaminating transfer, with which graphene is delaminated from the substrate. Then the origins of contamination are discussed followed with how contamination affects graphene properties. The main contaminations induced by transfer are ions from the etchant and electrolyte, undissolved metal or metal oxide particles, and organic residues from carrier films. Contaminations have a great influence on the electrical, thermal and optical properties of graphene. Then the up-to-date progress of techniques for clean transfer is reviewed, including modifying the cleaning process or using alternative etchant/electrolyte to remove or suppress metal contamination and annealing graphene or using alternative carrier films (e.g., more dissoluble materials) to remove or suppress organic residues. Finally, the challenges of clean transfer of graphene are summarized, and future research directions and opportunities are prospected. This review not only contributes to the research of graphene film transfer technology, but also has great reference value for the clean fabrication of the whole two-dimensional materials and devices.