There is an increasing number of rapidly growing repositories capturing the movement of people in space-time. Movement trajectory compression becomes an obvious necessity for coping with such growing data volumes. This paper introduces the concept of semantic trajectory compression (STC). STC allows for substantially compressing trajectory data with acceptable information loss. It exploits that human urban mobility typically occurs in transportation networks that define a geographic context for the movement. In STC, a semantic representation of the trajectory that consists of reference points localized in a transportation network replaces raw, highly redundant position information (e.g., from GPS receivers). An experimental evaluation with real and synthetic trajectories demonstrates the power of STC in reducing trajectories to essential information and illustrates how trajectories can be restored from compressed data. The paper discusses possible application areas of STC trajectories.