Fingerprinting is a method of embedding a traceable mark into digital data to (i) verify the owner and (ii) identify the recipient of a released copy of a data set. This is crucial when releasing data to third parties, especially if it involves a fee, or if the data is of sensitive nature and further sharing and leaks should be discouraged and deterred from. A fingerprint is required to (i) be robust against modifications t o t he d ata to achieve successful ownership protection, while (ii) affecting the quality and utility of the data as little as possible.So far, literature mostly assumes attackers with rather limited capabilities who perform random modification t o t he dataset. With a certain task in mind to perform on the data, the attacker can however perform an adaptive and targeted attack that maximises its chances of removing or invalidating the fingerprint, while reducing the data utility the least. In the same line, the data owner can optimise the robustness of the scheme by anticipating a specific f ocus o f t he a ttacker a nd f ocusing t he fingerprint embedding on the most valuable parts of the data. In this paper, we, therefore, provide an in-depth discussion on threat models, targeted attacks and adaptive defences. We further demonstrate the impact of targeted attacks on classical and, in comparison, adaptive fingerprinting i n a n e mpirical manner.