Face recognition and identity verification are now critical components of current security and verification technology. The main objective of this review is to identify the most important deep learning techniques that have contributed to the improvement in the accuracy and reliability of facial recognition systems, as well as highlighting existing problems and potential future research areas. An extensive literature review was conducted with the assistance of leading scientific databases such as IEEE Xplore, ScienceDirect, and SpringerLink and covered studies from the period 2015 to 2024. The studies of interest were related to the application of deep neural networks, i.e., CNN, Siamese, and Transformer-based models, in face recognition and identity verification systems. Deep learning-based approaches have been shown through cross-sectional studies to improve recognition accuracy under diverse environmental and demographic conditions. Anti-counterfeiting (Anti-Spoofing) and real presence detection features integrated into systems have likewise enhanced system security against advanced attacks such as 3D masks, false images and videos, and Deepfake technology. Future trends point to the need to develop deep, multi-sensory and interpretable learning models, and adopt learning strategies based on limited data, while adhering to legal and ethical frameworks to ensure fairness andtransparency.