This paper aims to provide a brief review of the feature extraction methods applied for finger vein recognition. The presented study is designed in a systematic way in order to bring light to the scientific interest for biometric systems based on finger vein biometric features. The analysis spans over a period of 13 years (from 2008 to 2020). The examined feature extraction algorithms are clustered into five categories and are presented in a qualitative manner by focusing mainly on the techniques applied to represent the features of the finger veins that uniquely prove a human’s identity. In addition, the case of non-handcrafted features learned in a deep learning framework is also examined. The conducted literature analysis revealed the increased interest in finger vein biometric systems as well as the high diversity of different feature extraction methods proposed over the past several years. However, last year this interest shifted to the application of Convolutional Neural Networks following the general trend of applying deep learning models in a range of disciplines. Finally, yet importantly, this work highlights the limitations of the existing feature extraction methods and describes the research actions needed to face the identified challenges.