Few-shot fine-grained image classification (FSFGIC) methods refer to machine learning methods which aim to classify images (e.g., bird species, flowers, and airplanes) belonging to subordinate object categories of the same entry-level category with only a few samples. It is worth to note that feature representation learning is used not only to represent training samples, but also to construct classifiers for performing various FSFGIC tasks. In this paper, starting from the definition of FSFGIC, a taxonomy of feature representation learning for FSFGIC is proposed. According to this taxonomy, we discuss key issues on FSFGIC (including data augmentation, local or/and global deep feature representation learning, class representation learning, and task specific feature representation learning). The existing popular datasets and evaluation standards are introduced. Furthermore, a novel classification performance evaluation mechanism is designed with a 0.95 confidence interval for judging whether the classification accuracy obtained by a certain specified method is good or bad. Moreover, current challenges and future trends of feature representation learning on FSFGIC are elaborated.