Applications based on biometric authentication have received a lot of interest in the last years due to the breathtaking results obtained using personal traits such as face or fingerprint. However, it is important not to forget that these biometric systems have to withstand different types of possible attacks. This chapter carries out an analysis of different Presentation Attack (PA) scenarios for on-line handwritten signature verification. The main contributions of this chapter are: i) an updated overview of representative methods for Presentation Attack Detection (PAD) in signature biometrics; ii) a description of the different levels of PAs existing in on-line signature verification regarding the amount of information available to the impostor, as well as the training, effort, and ability to perform the forgeries; and iii) an evaluation of the system performance in signature biometrics under different scenarios considering recent publicly available signature databases, DeepSignDB and SVC2021_EvalDB. This work is in line with recent efforts in the Common Criteria standardization community towards security evaluation of biometric systems.