Finger vein authentication is a reliable biometric method with advantages like resistance to forgery and environmental variations. This paper explores the use of Convolutional Neural Networks (CNNs) to improve the accuracy and robustness of finger vein authentication systems. CNNs can learn discriminative features from raw input data, improving the effectiveness of finger vein recognition in real-world scenarios. The review covers recent research on CNN-based approaches for finger vein authentication, including network architectures, feature extraction techniques, and training strategies. However, challenges such as large-scale training datasets and computational resources are discussed. Future research in CNN-based finger vein authentication should focus on exploring novel network architectures, improving generalization across diverse finger vein patterns, and addressing privacy and security concerns.