Fingerprints play a central role in any field where person identification is required. In forensics and biometrics, three-dimensional fingerprint-based imaging technologies, and corresponding recognition methods, have been vastly investigated. In cultural heritage, preliminary studies provide evidence that the three-dimensional impressions left on objects from the past (ancient fingerprints) are of paramount relevance to understand the socio-cultural systems of former societies, to possibly identify a single producer of multiple potteries, and to authenticate the artist of a sculpture. These findings suggest that the study of ancient fingerprints can be further investigated and open new avenues of research. However, the potential for capturing and analyzing ancient fingerprints is still largely unexplored in the context of cultural heritage research. In fact, most of the existing studies have focused on plane fingerprint representations and commercial software for image processing. Our aim is to outline the opportunities and challenges of digital fingerprint recognition in answering a range of questions in cultural heritage research. Therefore, we summarize the fingerprint-based imaging technologies, reconstruction methods, and analyses used in biometrics that could be beneficial to the study of ancient fingerprints in cultural heritage. In addition, we analyze the works conducted on ancient fingerprints from potteries and ceramic/fired clay sculptures. We conclude with a discussion on the open challenges and future works that could initiate novel strategies for ancient fingerprint acquisition, digitization, and processing within the cultural heritage community.