This article comprehensively surveys the development of trajectory data classification. Considering the critical role of trajectory data classification in modern intelligent systems for surveillance security, abnormal behavior detection, crowd behavior analysis, and traffic control, trajectory data classification has attracted growing attention. According to the availability of manual labels, which is critical to the classification performances, the methods can be classified into three categories, i.e., unsupervised, semi-supervised, and supervised. Furthermore, classification methods are divided into some sub-categories according to what extracted features are used. We provide a holistic understanding and deep insight into three types of trajectory data classification methods and present some promising future directions