Several works have been proposed in the last few years for raw trajectory data analysis, and some attempts have been made to define trajectories from a more semantic point of view. Semantic trajectory data analysis has received significant attention recently, but the formal definition of semantic trajectory, the set of aspects that should be considered to semantically enrich trajectories and a conceptual data model integrating these aspects from a broad sense is still missing. This article presents a semantic trajectory conceptual data model named CONSTAnT, which defines the most important aspects of semantic trajectories. We believe that this model will be the foundation for the design of semantic trajectory databases, where several aspects that make a trajectory “semantic” are taken into account. The proposed model includes the concepts of semantic subtrajectory, semantic points, geographical places, events, goals, environment and behavior, to create a general concept of semantic trajectory. The proposed model is the result of several years of work by the authors in an effort to add more semantics to raw trajectory data for real applications. Two application examples and different queries show the flexibility of the model for different domains.