Facial biometrics has been recently received tremendous attention as a convenient replacement for traditional authentication systems. Consequently, detecting malicious attempts has found great significance, leading to extensive studies in face anti-spoofing (FAS),i.e., face presentation attack detection. Deep feature learning and techniques, as opposed to hand-crafted features, have promised dramatic increase in the FAS systems' accuracy, tackling the key challenges of materializing realworld application of such systems. Hence, a new research area dealing with development of more generalized as well as accurate models is increasingly attracting the attention of the research community and industry. In this paper, we present a comprehensive survey on the literature related to deep-feature-based FAS methods since 2017. To shed light on this topic, a semantic taxonomy based on various features and learning methodologies is represented. Further, we cover predominant public datasets for FAS in a chronological order, their evolutional progress, and the evaluation criteria (both intra-dataset and inter-dataset). Finally, we discuss the open research challenges and future directions.