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This paper gives a survey about numismatic research fields where computer vision methods have the potential to improve the effectiveness and impact of research work. In total, five different parts of numismatic research areas are identified: the classification of coins into given types, the identification of concrete coin specimens, the identification of coins struck by the same die, the reassembling of broken coin fragments and the segmentation and surveying of coins. For each application a problem description is given and the use of computer vision methods is discussed in detail. Additionally, for the image-based classification, identification and segmentation of coins results achieved so far are presented. Since computer vision methods are applied on photographs of coins, their acquisition (both in 2D and 3D) is covered as well.