Finger vein recognition is an emerging biometric recognition technology. Different from the other biometric features on the body surface, the venous vascular tissue of the fingers is buried deep inside the skin. Due to this advantage, finger vein recognition is highly stable and private. They are almost impossible to be stolen and difficult to interfere with by external conditions. Unlike the finger vein recognition methods based on traditional machine learning, the artificial neural network technique, especially deep learning, it without relying on feature engineering and have superior performance. To summarize the development of finger vein recognition based on artificial neural networks, this paper collects 149 related papers. First, we introduce the background of finger vein recognition and the motivation of this survey. Then, the development history of artificial neural networks and the representative networks on finger vein recognition tasks are introduced. The public datasets that are widely used in finger vein recognition are then described. After that, we summarize the related finger vein recognition tasks based on classical neural networks and deep neural networks, respectively. Finally, the challenges and potential development directions in finger vein recognition are discussed. To our best knowledge, this paper is the first comprehensive survey focusing on finger vein recognition based on artificial neural networks.