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Analysis of trajectory data is the key to a growing number of applications aiming at global understanding and management of complex phenomena that involve moving objects (e.g. worldwide courier distribution, city traffic management, bird migration monitoring). Current DBMS support for such data is limited to the ability to store and query raw movement (i.e. the spatio-temporal position of an object). This paper explores how conceptual modeling could provide applications with direct support of trajectories (i.e. movement data that is structured into countable semantic units) as a first class concept. A specific concern is to allow enriching trajectories with semantic annotations allowing users to attach semantic data to specific parts of the trajectory. Building on a preliminary requirement analysis and an application example, the paper proposes two modeling approaches, one based on a design pattern, the other based on dedicated data types, and illustrates their differences in terms of implementation in an extended-relational context.