It is widely acknowledged that the integration of BIM and GIS data is a crucial step forward for future 3D city modelling, but most of the research conducted so far has covered only the semantic aspects of GIS-BIM integration. We present here the results of the GeoBIM project, in which we tackled three integration problems focussing instead on aspects involving geometry processing: (i) the automated processing of complex architectural IFC models, (ii) the integration of existing GIS subsoil data in BIM, and (iii) the georeferencing of BIM models for their use in GIS software. All the problems have been studied using real world models and existing datasets made and used by practitioners in the Netherlands. For each problem, we expose in detail the issues we faced, our proposed solutions, and our recommendations for a more successful integration.