Topological relationships between spatial objects represent important knowledge that users of geographic information systems expect to retrieve from a spatial database. A difficult task is to assign precise semantics to user queries involving concepts such as crosses, is inside, is adjacent. In this paper, we present two methods for describing topological relationships. The first method is an extension of the geometric point-set approach by taking the dimension of the intersections into account. This results in a very large number of different topological relationships for point, line, and area features. In the second method, which aims to be more suitable for humans, we propose to group all possible cases into a few meaningful topological relationships and we discuss their exclusiveness and completeness with respect to the point-set approach.