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Fingerprint authentication systems are highly vulnerable to artificial reproductions of fingerprint, called fingerprint presentation attacks. Detecting presentation attacks is not trivial because attackers refine their replication techniques from year to year. The International Fingerprint liveness Detection Competition (LivDet), an open and well-acknowledged meeting point of academies and private companies that deal with the problem of presentation attack detection, has the goal to assess the performance of fingerprint presentation attack detection (FPAD) algorithms by using standard experimental protocols and data sets. Each LivDet edition, held biannually since 2009, is characterized by a different set of challenges against which competitors must be dealt with. The continuous increase of competitors and the noticeable decrease in error rates across competitions demonstrate a growing interest in the topic. This paper reviews the LivDet editions from 2009 to 2021 and points out their evolution over the years., Comment: Chapter of the Handbook of Biometric Anti-Spoofing (Third Edition)