Biometric authentication has garnered significant attention as a secure and efficient method of identity verification. Among the various modalities, hand vein biometrics, including finger vein, palm vein, and dorsal hand vein recognition, offer unique advantages due to their high accuracy, low susceptibility to forgery, and non-intrusiveness. The vein patterns within the hand are highly complex and distinct for each individual, making them an ideal biometric identifier. Additionally, hand vein recognition is contactless, enhancing user convenience and hygiene compared to other modalities such as fingerprint or iris recognition. Furthermore, the veins are internally located, rendering them less susceptible to damage or alteration, thus enhancing the security and reliability of the biometric system. The combination of these factors makes hand vein biometrics a highly effective and secure method for identity verification.This review paper delves into the latest advancements in deep learning techniques applied to finger vein, palm vein, and dorsal hand vein recognition. It encompasses all essential fundamentals of hand vein biometrics, summarizes publicly available datasets, and discusses state-of-the-art metrics used for evaluating the three modes. Moreover, it provides a comprehensive overview of suggested approaches for finger, palm, dorsal, and multimodal vein techniques, offering insights into the best performance achieved, data augmentation techniques, and effective transfer learning methods, along with associated pretrained deep learning models. Additionally, the review addresses research challenges faced and outlines future directions and perspectives, encouraging researchers to enhance existing methods and propose innovative techniques.