Although fingerprint verification systems reached a high degree of accuracy, it has been recently shown that they can be circumvented by “fake fingers”, namely, fingerprint images coming from stamps reproducing an user fingerprint, which is processed as an “alive” one. Several methods have been proposed for facing with this problem, but the issue is far from a final solution. Since the problem is relevant both for the academic and the industrial communities, in this paper, we present a critical review of current approaches to fingerprint vitality detection in order to analyze the state–of–the art and the related open issues.