Biometric systems are prevalent in access control but are vulnerable to frauds. A typical attempt of violating them is through presentation attacks, in which synthetic data is directly presented to an acquisition sensor to deceive these systems. A well-designed biometric system should have a presentation attack detection (PAD) module. A fruitful way to perform PAD is to model properties of peculiar traits (artifacts) in synthetic data. Studies have been advocating for approaches that seek to model the artifacts automatically from data (data-driven), achieving state-of-the-art results in PAD. However, the following questions arise from this literature: Which approaches are state of the art? When do these approaches fail? How can such approaches complement the proposed ones based on human knowledge on PAD? How robust are these approaches under cross-dataset scenarios? Are these approaches robust against new attack types (e.g., face morphing)? Do these methods provide other ways to perform PAD, for example, using open-set classifiers rather than the classical binary formulation? Are these methods applicable to the multi-biometric setting? In this chapter, we address these questions through a literature review, focusing on three biometric modalities: face, fingerprint, and iris.