The rapid development of location-aware applications and services poses new challenges for trajectory data mining. The raw trajectory data usually consist of ordered sequences of coordinate-timestamp tuple, while many algorithms widely used for data analysis require input data to be in vector space. Therefore, it is an important and necessary step to effectively represent trajectory data from variable-length coordinate-timestamp sequence to a fixed-length vector that maintains the spatial-temporal characteristics of the movement. Most conventional trajectory representation methods are based on feature engineering, in which trajectory representation is usually considered as part of the data preprocessing. With the prevalence of deep learning, the ability of learning from large-scale data endows deep learning-based methods for trajectory representation with more potential and vitality, which achieved better performance compared to traditional methods. This paper provides a comprehensive review of recent progress in trajectory representation and summarizes the trajectory representation methods into two categories according to the different scales:trajectory unit representation and entire trajectory representation. In each category, the methods of different principles are compared and analyzed. Among them, the methods based on trajectory point are emphasized, and also the widely used methods based on neural networks are systematically classified. Besides, the applications related to trajectory representation under each category are introduced. Finally, the future research directions are pointed out in the field of trajectory representation.