The Topic Group 7 of CERME-3 on “Geometrical Thinking” had more than 20 participants from countries all over Europe and from Mexico. During its sessions, the participants implicitly discussed 10 papers prepared for the Topic Group. No formal presentations of the 10 papers were made, but every author had a chance to present her/his main ideas. This report does not follow the order of the discussion in the group, but tries to account for the arguments brought forward and commented according to the structure given by the headings of the sections of the report.