As a new biometric technique, finger vein recognition has attracted lots of attention from research groups and industry at home and abroad, and shows great market potentials. This paper introduces main current researches on finger vein recognition, including finger vein imaging principle and image enhancement techniques, feature extraction methods， finger vein related multi-feature and multi-model fusion methods. Feature extraction methods are described comprehensively, and classified into four categories, i.e., vein pattern feature, texture feature, minutiae feature, and learned feature by machine learning methods. Based on these analyses, we further summary some challenges in finger vein recognition and its applications, including lowering the price of imaging device, improving the quality of image, and decreasing the effect from low quality image, the finger displacement, large scale populations and outdoor image acquisition. And we hope that the challenges can inspire some new ideas in the future.