Cell complexes have extensively been used as a compact representation of both the geometry and topology of shapes. They have been the basis modeling tool for boundary representations of 3D shapes, and several dimension-specific data structures and modeling operators have been proposed in the literature. Here, we propose basic topological modeling operators for building and updating cell complexes in arbitrary dimensions. These operators either preserve the topology of the cell complex, or they modify it in a controlled way. We compare these operators with the existing ones proposed in the literature, in particular with handle operators and various Euler operators on 2D and 3D cell complexes.