A semantic trajectory is a combination of a spatiotemporal trajectory and semantic information. Besides spatiotemporal information, a semantic trajectory comprises movement states (e.g. speed, direction), external contextual information (e.g. temperature, spatial topological relationships), and social relationships (e.g. friend relationships, social activities) of moving objects. We can derive from semantic trajectories intentions, habits, emotions, and other high order semantic information, thus further discover the patterns, relationships, and rules of individual or collective mobility behaviors. Therefore, compared with spatiotemporal trajectories, semantic trajectories are more in line with the practical requirements of decision-making applications in terms of semantics, interpretation, feasibility, and so on. This paper reviews the key technologies of semantic trajectory mining. First, we introduce the concept of semantic trajectories, and summarize four classic types of semantic trajectory definitions according to semantic elements. Then, we introduce the main phases of semantic trajectory modeling, including preprocessing, trajectory segmentation, and semantic enrichment. Since semantic trajectories cannot be acquired from location-acquisition devices as spatiotemporal trajectories, semantic trajectories need to be obtained through modeling techniques. Thus, the basic idea is to combine spatiotemporal trajectories with semantic information to generate corresponding semantic trajectories. Next, we introduce the main tasks of semantic trajectory mining, including semantic trajectory pattern mining, semantic trajectory clustering, semantic trajectory classification, anomaly detection of semantic trajectories, and so on. For each mining task, this paper introduces the basic principles and related algorithms, and summarizes the main key technologies and challenges. Finally, this paper concludes with the existing challenges and promising research directions of semantic trajectory mining. Specifically, this paper discusses the important research issues of semantic trajectory modeling in aspects including modeling definition, semantic annotation technologies, and multi-source data modeling. This paper also discusses the promising research issues of semantic trajectory mining such as semantic trajectory data management, classification and prediction, trajectory stream mining, privacy protection, multi-granularity mining, and evaluation methods.