In this paper we discuss two data models for spatial database systems: the linear data model and the topological data model. Both can be used to model a wide range of applications. The linear data model is particularly suited to model spatial database applications in which exact geometrical information is required and in which this information can be approximated by linear geometrical spatial objects. The topological model on the other hand is suitable for applications in which rather than exact geometrical information the relative position of spatial objects is of importance. We will specify in each case which types of spatial data and spatial databases are under consideration. A semantics for both data models is formally defined in terms of finite representations of spatial databases in the data models. We also present languages to query spatial databases in both models and briefly investigate their expressiveness.