Fingerprints being the most widely employed biometric trait, due to their high acceptability and low sensing cost, have replaced the traditional methods of human authentication. Although, the deployment of these biometrics-based recognition systems is accelerating, they are still susceptible to spoofing attacks where an attacker presents a fake artifact generated from silicone, candle wax, gelatin, etc. To safeguard sensor modules from these attacks, there is a requirement of an anti-deception mechanism known as fingerprint spoof detectors (FSD) also known as anti-spoofing mechanisms. A lot of research work has been carried out to design fingerprint anti-spoofing techniques in the past decades and currently, it is oriented towards deep learning (DL)-based modeling. In the field of fingerprint anti-spoofing, since the 2014, the paradigm has shifted from manually crafted features to deep features engineering. Hence, in this study, we present a detailed analysis of the recent developments in DL based FSDs. Additionally, we provide a brief comparative study of standard evaluation protocols that include benchmark anti-spoofing datasets as well as performance evaluation metrics. Although significant progress has been witnessed in the field of DL-based FSDs, still challenges are manifold. Therefore, we investigated these techniques critically to list open research issues along with their viable remedies that may put forward a future direction for the research community. The majority of the research work reveals that deep feature extraction for fingerprint liveness detection demonstrates promising performance in the case of cross-sensor scenarios. Though convolution neural network (CNN) models extract deep-level features to improve the classification accuracy, their increased complexity and training overhead is a tradeoff between both the parameters. Furthermore, enhancing the performance of presentation attack detection (PAD) techniques in the cross-material scenario is still an open challenge for researchers.